
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 \( \triangle ABC \), the coordinates of vertex \( A \) are \( A(1,4) \). The equation of the angle bisector of \( \angle ABC \) is \( x - 2y = 0 \) and the equation of the angle bisector of \( \angle ACB \) is \( x + y - 1 = 0 \). Find the equation of the line \( BC \).

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