
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
A function \( f(x) \) defined on \(\mathbb{R}\) satisfies the following conditions for any real number \( x \):
$$
\begin{array}{l}
f(x+3) \leqslant f(x) + 3, \\
f(x+2) \geqslant f(x) + 2,
\end{array}
$$

and \( f(1) = 2 \). Let \( a_{n} = f(n) \) for \( n \in \mathbb{Z}_{+} \). Find:
$$
f(2015) =
$$

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