
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
Given a sequence $\{ a_{n} \}$, the first term is $a_{1}=1$, $a_{2}=3$, and for any $n \in \mathbb{N}^{+}$, it satisfies $(a_{n+1}-a_{n} \leqslant 2^{n})$ and $(a_{n+2}-a_{n} \geqslant 3 \times 2^{n})$. Find the value of $a_{2015}$.

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