
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 \( f(x) \) is defined on the set of real numbers. For any \( x, y \in \mathbf{R} \), it satisfies the equation \( f(x+y) + f(x-y) = 2 f(x) \cdot f(y) \), and \( f(0) \neq 0 \).

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