
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
Let  $A,B,C,D$ , be four different points on a line  $\ell$ , so that  $AB=BC=CD$ . In one of the semiplanes determined by the line  $\ell$ , the points  $P$  and  $Q$  are chosen in such a way that the triangle  $CPQ$  is equilateral with its vertices named clockwise. Let  $M$  and  $N$  be two points of the plane be such that the triangles  $MAP$  and  $NQD$  are equilateral (the vertices are also named clockwise). Find the angle  $\angle MBN$ .

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