
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 p: the equation $x^2+2mx+1=0$ has two distinct positive roots; q: the equation $x^2+2(m-2)x-3m+10=0$ has no real roots. Find the range of real numbers $m$ for which $p \lor q$ is true and $p \land q$ is false.

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