
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
Let the arithmetic sequence $\{a_n\}$ consist of integers, with a common difference $d \neq 0$, and $a_5 = 6$. If the infinite sequence $a_3, a_5, a_{n_1}, a_{n_2}, \ldots, a_{n_t}, \ldots$ ($5 < n_1 < n_2 < \ldots < n_t < \ldots$) forms a geometric sequence, then the number of terms in the first 2015 terms of the sequence $\{a_n\}$ that are also in this geometric sequence is $\boxed{\text{\_\_\_\_\_\_}}$.

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