
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 $\bigtriangleup ABC$, $AB = 84$, and $AC = 91$. A circle with center $A$ and a radius equal to $AB$ intersects $\overline{BC}$ at points $B$ and $X$. Both $\overline{BX}$ and $\overline{CX}$ have integer lengths. Determine the length of $BC$.
- **A)** $1225$ 
- **B)** $245$ 
- **C)** $49$ 
- **D)** $175$ 
- **E)** $35$

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