
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 the real numbers \( a \), \( b \), and \( c \) such that \( f(x) = a \cos x + b \cos 2x + c \cos 3x \geq -1 \) holds for any real number \( x \), find the maximum value of \( a + b + c \).

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