
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 the function $f(x)=x^{2}+a\cos x$, where $a\in\mathbb{R}$, and the non-empty set $M=\{x|f(x)=0,x\in\mathbb{R}\}$.
- The sum of all elements in $M$ is \_\_\_\_\_\_.
- If the set $N=\{x|f(f(x))=0,x\in\mathbb{R}\}$, and $M=N$, then the value of $a$ is \_\_\_\_\_\_.

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