
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 \( f(x) \) be a real-valued function of the real variable \( x \), and \( f(x) \) is not identically zero. For all \( a \) and \( b \), \( f(a+b) + f(a-b) = 2f(a) + 2f(b) \). It is also given that \( f(2) = 9 \). Determine the value of \( f(4) \).

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