
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
Consider the propositions p and q, where $p$ is "For all $x \in [0,1], x^2 - m \le 0$" and $q$ is "The equation $\frac{x^2}{m^2} + \frac{y^2}{4} = 1$ represents an ellipse with foci on the x-axis."
1. If the negation of $p$ is false, find the range of the real number $m$.
2. If the disjunction $p \lor q$ is true and the conjunction $p \land q$ is false, find the range of the real number $m$.

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