
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
Assuming the proposition $f(x) = x^2 + (2m - 2)x + 3$ is a decreasing function on the interval $(-\infty, 0)$; and the proposition $q$: "The inequality $x^2 - 4x + 1 - m \leq 0$ has no solution." If the proposition $p \vee q$ is true, and the proposition $p \wedge q$ is false, find the range of the real number $m$.

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