
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 $m\in \mathbb{R}$, let $p: \forall x \in [-1,1]$, $x^2-2x-4m^2+8m-2\geqslant 0$ holds; $q: \exists x \in [1,2]$, $\log_{\frac{1}{2}}(x^2-mx+1) < -1$ holds. If "$p \vee q$" is true and "$p \wedge q$" is false, find the range of $m$.

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