
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 $f(x)=a\ln x+x^{2}+bx+1$, the equation of the tangent line at the point $(1,f(1))$ is $4x-y-12=0$.
(1) Find the analytic expression of the function $f(x)$;
(2) Find the monotonic intervals and extreme values of $f(x)$.

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