
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
(13 points) Given the function $f(x) = x^3 + mx^2 + nx - 2$ whose graph passes through the point $(-1, -6)$, and the function $g(x) = f'(x) + 6x$ whose graph is symmetric about the y-axis.  
(1) Find the values of $m$ and $n$ and the intervals of monotonicity for the function $y = f(x)$.  
(2) If $a > 0$, find the extremum of the function $y = f(x)$ in the interval $(a - 1, a + 1)$.

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