
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 $ABC$, vertex $A(2,1)$, $B(-1,-1)$, and the equation of the line containing the angle bisector of $\angle C$ is $x+2y-1=0$.
(1) Find the coordinates of point $C$;
(2) Find the distance from point $A$ to line $BC$.

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