
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 the function $f(x) = \frac{1}{\sqrt{x+2}} + \log(3-x)$, its domain is set $A$, and set $B = \{x | 1-m < x < 3m-1\}$.
(1) Find the set $A$,
(2) If $A \cap B = B$, find the range of the real number $m$.

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