
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
Triangle \(ABC\) satisfies \(\angle B > \angle C\). Let \(M\) be the midpoint of \(BC\), and let the perpendicular bisector of \(BC\) meet the circumcircle of \(\triangle ABC\) at a point \(D\) such that points \(A\), \(D\), \(C\), and \(B\) appear on the circle in that order. Given that \(\angle ADM = 68^\circ\) and \(\angle DAC = 64^\circ\), find \(\angle B\).

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