
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 function \(f(x) = x^2 + a x + b \cos x\), suppose \(\{x \mid f(x) = 0, x \in \mathbf{R}\} = \{x \mid f(f(x)) = 0, x \in \mathbf{R}\} \neq \varnothing\). Find all real values of \(a\) and \(b\) that satisfy this condition.

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