
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 \(\mathbf{R}\) satisfies
\[
f\left(\frac{2a + b}{3}\right) = \frac{2f(a) + f(b)}{3} \quad (a, b \in \mathbf{R}),
\]
with \( f(1) = 1 \) and \( f(4) = 7 \). Find \( f(2015) \).

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