
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 $f(x)=x^2+ax+b\cos x$, and given that $\{x|f(x)=0, x\in \mathbb{R}\}=\{x|f(f(x))=0, x\in \mathbb{R}\}\neq \emptyset$, then the values of all real numbers $a$ and $b$ that satisfy the condition are respectively __________.

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