
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
In triangle $ABC$, it is known that $A(0,2)$, $B(2,0)$, and $C(-2,-1)$  
(1) Find the equation of the line on which the height $AH$ from $A$ to side $BC$ lies;  
(2) Find the area of triangle $ABC$.

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