
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
The proposition p: "For all $x \in [0, \frac{\pi}{4}]$, $\tan(x) \leq m$" holds true for all $x$ in the range. The proposition q: "Given the functions $f(x) = x^2 + m$ and $g(x) = \left(\frac{1}{2}\right)^x - m$, for every $x_1 \in [-1, 3]$, there exists some $x_2 \in [0, 2]$ such that $f(x_1) \geq g(x_2)$" also holds. If the statement $p \land q$ is false and $p \lor q$ is true, determine the range of values for $m$.

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