
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 a function $f(x)$ defined on $\mathbb{R}$ satisfies $f(x_{1}+x_{2})=f(x_{1})+f(x_{2})$, and when $x \gt 0$, $f(x) \gt 0$, $f(1)=1$. Determine the solution set of the inequality $2^{1+f(x)}+2^{1-f(x)}+2f(x^{2})\leqslant 7$ with respect to $x$.

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