
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
Let set $A = \{x \mid (x - 2m + 1)(x - m + 2) < 0\}$, $B = \{x \mid 1 \leq x + 1 \leq 4\}$.
(1) If $m = 1$, find $A \cap B$;
(2) If $A \cap B = A$, find the set of all possible real numbers for $m$.

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