
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 $p$ be the proposition that there exists an $x_0 \in \mathbb{R}$ such that $x_0^2 + 2(m-3)x_0 + 1 < 0$, and $q$ be the proposition that for all $x \in \mathbb{R}$, $4x^2 + 4(m-2)x + 1 > 0$ always holds. If $p \vee q$ is true and $p \wedge q$ is false, find the range of values for $m$.

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