
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 \( a_{n} = 2^{n} \) and \( b_{n} = 5n - 1 \) for \( n \in \mathbb{Z}_{+} \).

Define the set \( S = \left\{a_{1}, a_{2}, \cdots, a_{2015}\right\} \cap \left\{b_{1}, b_{2}, \cdots, b_{a_{2015}}\right\} \).

Find the number of elements in the set \( S \).

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