
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 proposition p: For all $m \in [-1, 1]$, the inequality $a^2 - 5a + 7 \geq m + 2$ always holds; proposition q: The equation $x^2 + ax = 2 = 0$ has two distinct real roots. If $p \lor q$ is true, and $p \land q$ is false, find the range of real numbers for $a$.

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