
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
Let $m$ be a real number. Given proposition $p$: The minimum value of the function $f(x) = x^2 - 2x + m^2 + 3m - 3$ is less than 0; and proposition $q$: The equation $\frac{x^2}{5m-1} - \frac{y^2}{m-2} = 1$ represents an ellipse with foci on the $x$-axis. If $p \vee q$ is a false proposition and $p \wedge q$ is a false proposition, find the range of values for $m$.

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