
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 that one of the roots of the quadratic function $f(x)=ax^{2}+bx+c$ is $-1$, and it always satisfies $\[f(x)-x\]⋅\[f(x)- \frac {x^{2}+1}{2}\]\leqslant 0$.

(1) Find the value of $f(1)$;

(2) Find the analytic expression of $f(x)$.

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