
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 propositions p and q:
- p: For all x in $[-1, 0]$, $\log_2(x + 2) < 2m$
- q: The quadratic equation $x^2 - 2x + m^2 = 0$ has two distinct real roots.
Find the range of real number $m$ under the following conditions:
1. $(\lnot p) \land q$ is a true proposition.
2. $p \lor q$ is a true proposition, and $p \land q$ is a false proposition.

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