
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
The problem of solving systems of linear congruences first appeared in the Chinese mathematical work "Sunzi's Mathematical Classic" during the Southern and Northern Dynasties (5th century AD), in the 26th problem of the second volume, called "Problems in which the number of objects is unknown." The original text states: "There are an unknown number of objects. When counted by threes, two are left over; when counted by fives, there are three left over. How many objects are there?" In other words, we are seeking an integer that when divided by three yields a remainder of two and when divided by five yields a remainder of three. If this integer $a$ is within the range $a\in[2,2019]$, find how many such integers $a$ satisfy these conditions.

Present the answer in LaTex format: \boxed{Your answer}
user