
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 $f(x)=x^2+bx+c$ is an even function, and the curve $y=f(x)$ passes through the point $(2,5)$, $g(x)=(x+a)f(x)$.  
(1) Find the tangent line of the curve $y=g(x)$ that has a slope of 0, and determine the range of the real number $a$.  
(2) If the function $y=g(x)$ reaches an extremum when $x=-1$, determine the monotonic intervals of $y=g(x)$.

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