
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
Consider triangle \(ABC\) with side lengths \(AB=4\), \(BC=7\), and \(AC=8\). Let \(M\) be the midpoint of segment \(AB\), and let \(N\) be the point on the interior of segment \(AC\) that also lies on the circumcircle of triangle \(MBC\). Compute \(BN\).

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