
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 $f(x)= \begin{cases} x\ln (1+x)+x^{2}, & x\geqslant 0 \\ -x\ln (1-x)+x^{2}, & x < 0 \end{cases}$, if $f(-a)+f(a)\leqslant 2f(1)$, determine the range of the real number $a$.

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