
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
Determine the range of the real number $m$ such that the proposition $p \vee q$ is true and $p \wedge q$ is false, given that $p$ is the proposition "The equation $x^2 + 2mx + 1 = 0$ has two distinct positive roots" and $q$ is the proposition "The equation $x^2 + 2(m-2)x - 3m + 10 = 0$ has no real roots".

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