
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 function $f(x)=e^{ax}+bx (a < 0)$ whose tangent line at the point $(0,f(0))$ is $y=5x+1$, and $f(1)+f'(1)=12$.
(I) Find the extreme values of the function $y=f(x)$;
(II) If $f(x) > x^{2}+3$ holds true for $x\in[1,m]$, find the maximum value of the positive integer $m$.

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