
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 $ABC$, $AB = 74$, and $AC = 88$. A circle with center $A$ and radius $AC$ intersects line $BC$ at points $C$ and $Y$. Both $BY$ and $CY$ are integers in length. What is the length of $BC$?
A) 98
B) 127
C) 162
D) 104
E) 173

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