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Operatives, in the past you have seen sentences like this:

Tiberius inquit, "Lapis est in Aegyptiō."
Tiberius says, "The Lapis is in Egypt."

Salvius putat, "Recentiī ad Rōmam vēnērunt."
Salvius thinks, "The Recentii have come to Rome."

These are direct statements, made in writing by the use of quotations. In each example, the speakers, Tiberius and Salvius respectively, are making a direct statement. They are actually saying something. Now look at these next examples in which the speaker reports what someone hears, thinks, says etc:

Tiberius dīcit Lapidem esse in Aegyptiō.
Tiberius says that the Lapis is in Egypt.

Salvius putat Recentiōs vēnisse ad Rōmam.
Salvius thinks that the Recentii have come to Rome.

These examples are called indirect statements. Sometimes called the accusative and infinitive construction, indirect statements are introduced by verbs of mental or verbal action and are then followed by a subject accusative and an infinitive. In translation, it makes sense to translate the infinitive in an indirect statement as if it were a finite verb. Look at this example:

Clodia dīcit omnēs puellās gerere pulchrās stolās.
Clodia says that all the girls are wearing pretty dresses.

In the example above, the verb dicit, a verb of verbal action, introduces the indirect statement. Omnes puellas, in the accusative case, are the object of dicit, but the subject of gerere and pulchras stolas are the object of the infinitive gerere.

Here is a list of verbs which most commonly introduce indirect statements.

arbitrārī - to think
audīre - to hear
cognoscere - to recognize
crēdere - to believe
dīcere - to say
intellegere - to know, understand
negāre - to deny
putāre - to think
scīre - to know
sentīre - to feel, perceive
sperāre - to hope
vidēre - to see

There is an important rule to remember when dealing with indirect statements and translating them. If the infinitive in the indirect statement is in the present tense, then it happens at the same time as the main verb of the sentence. If the infinitive in the indirect statement is in the past tense, then it happened before the action of the main verb of the sentence. Look at the following examples:

Recentiī vidēbant mīlitēs comprehendere cīvēs.
The Recentii were seeing that the soldiers were arresting the citizens.

In this example, although the infinitive comprehendere is in the present tense, it is translated at the same time as the main verb of the sentence, videbant, which is in the imperfect tense.

Recentiī crēdēbant mīlitēs comprehendisse cīvēs.
The Recentii were believing that the soldiers had arrested the citizens.

In this example the infinitive is translated in the past relative to the main verb of the sentence because the infinitive itself is in the perfect tense.

Operatives, it is very simple. In indirect statements, infinitives in the present tense are translated at the same time as the main verb, those is the perfect tense at a time before the main verb, and those in the future tense at a time after the main verb.

Here are a few video briefings to explore: