
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 \( \triangle ABC \), \( AB = 86 \), and \( AC = 97 \). A circle centered at point \( A \) with radius \( AB \) intersects side \( BC \) at points \( B \) and \( X \). Moreover, \( BX \) and \( CX \) have integer lengths. What is the length of \( BC \)?

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