
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
For the function $f(x) = x^3 + mx^2 + nx - 2$, it is known that its graph passes through the point $(-1, -6)$, and the graph of the function $g(x) = f'(x) + 6x$ is symmetric about the y-axis.

(1) Find the values of $m$ and $n$ and the intervals where $y = f(x)$ is monotonic;
(2) If the function $h(x) = f(x) - ax$ is monotonically decreasing in the interval $(-1, 1)$, determine the range of the real number $a$.

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