
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 set $$A=\{0, 1, \log_{3}(m^{2}+2), m^{2}-3m\}$$, let $f: x \rightarrow 2x-3$ be a mapping from set $C=\{-1, 1, n\}$ to set $B=\{-5, -1, 3\}$.  
(1) If $m=5$, find $A \cap C$;  
(2) If $-2 \in A$, find the value of $m$.

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