
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 a square and \(S\) a point outside the square \(A B C D\) such that the triangle \(B C S\) is equilateral. Let \(N\) be the midpoint of the segment \([A S]\) and \(H\) the midpoint of the segment \([C D]\). Let \(P\) be the midpoint of the segment \([B S]\).

1) Calculate the angle \(\widehat{B P N}\).
2) Calculate the angle \(\widehat{N H C}\).

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