
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
Define the odd function $f(x)$ on $\mathbb{R}$. When $x \in (-\infty, 0)$, $f(x) = -x^2 + mx - 1$.

1. Find the analytic expression of $f(x)$ when $x \in (0, +\infty)$.
2. If the equation $f(x) = 0$ has five distinct real roots, find the range of the real number $m$.

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