
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
(1) Calculate: $\int_{-2}^{2}{\sqrt{4-{x}^{2}}}dx=$\_\_\_\_\_\_\_\_\_\_\_\_.

(2) If $f(x)+\int_{0}^{1}{f(x)dx=2x}$, then $f(x)=$\_\_\_\_\_\_\_\_\_\_\_\_.

(3) Arranging $3$ volunteers to complete $4$ tasks, with each person completing at least one task and each task being completed by one person, the total number of different arrangements is \_\_\_\_\_\_\_\_\_\_.

(4) Let the function $f(x)=x\ln({e}^{x}+1)- \frac{1}{2}{x}^{2}+3, x\in[-t,t](t > 0)$, if the maximum value of the function $f(x)$ is $M$ and the minimum value is $m$, then $M+m=$\_\_\_\_\_\_\_\_\_\_\_\_\_.

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