
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: In $\triangle ABC$, $A(3,3)$, $B(2,-2)$, $C(-7,1)$.  
Find: (1) The equation of the line containing the altitude $CH$ from $C$ to side $AB$.  
(2) The equation of the line containing the median $CM$ from $C$ to side $AB$.

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