
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
$18.$ Given the quadratic function $f(x)=ax^{2}+bx+c$ satisfies $f(0)=1$, for any $x∈R$, there is $1-x \leqslant f(x)$, and $f(x)=f(1-x)$.

(I) Find the analytical expression of the function $f(x)$;

(II) If there exists $x∈[-2,2]$ such that the equation $f(x)+2x=f(m)$ holds, find the range of values for the real number $m$.

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