
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 quadratic function $f(x)=x^{2}+mx+n$.
(1) If $f(x)$ is an even function with a minimum value of $1$, find the analytic expression of $f(x)$;
(2) Under the condition of (1), for the function $g(x)= \frac {6x}{f(x)}$, solve the inequality $g(2^{x}) > 2^{x}$ with respect to $x$;
(3) For the function $h(x)=|f(x)|$, if the maximum value of $h(x)$ is $M$ when $x\in[-1,1]$, and $M\geqslant k$ holds for any real numbers $m$ and $n$, find the maximum value of $k$.

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