
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 $f(x)=x^{2}+bx+c$ is an even function with one of its zero points being $1$, and the line $y=kx+m (k > 0)$ is tangent to the graph of $y=f(x)$.
(I) Find the analytic expression of the function $y=f(x)$;
(II) Find the maximum value of $mk$.

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