
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 $p$: The inequality $\int_{0}^{x} (2t+1) \, dt - m > 0$ holds for any $x \in [1, 2]$; $q$: For $f(x) = \begin{cases} x^2, & x \geq 0 \\ x-1, & x < 0 \end{cases}$, the inequality $f(m^2) > f(m+2)$ holds. If $p \lor q$ is true and $p \land q$ is false, find the range of $m$.

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