
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 that one vertex of △ABC is A(2,1), the angle bisector of ∠ACB lies on the line y=3x, and the midpoint of AC is on the line $y=- \frac {1}{7}x+3$. Find:
(1) The coordinates of vertex C;
(2) The equation of line BC.

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