
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 $\bigtriangleup ABC$, $AB = 75$, and $AC = 85$. A circle with center $A$ and radius $AB$ intersects $\overline{BC}$ at points $B$ and $X$. Moreover, $\overline{BX}$ and $\overline{CX}$ have integer lengths. What is $BC$?
**A)** 64
**B)** 80
**C)** 89
**D)** 120
**E)** 160

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