
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 propositions $p$: the equation $\frac{x^{2}}{m-2}+ \frac{y^{2}}{m-5}=1$ represents a hyperbola, and $q$: $x \in (0,+\infty)$, $x^{2}-mx+4 \geqslant 0$ always holds true. If $p \vee q$ is a true proposition and $(p \wedge q)$ is also true, find the range of values for $m$.

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