
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 an acute triangle  $ABC$ , we define  $D$  is the projection of  $A$  on the side  $BC$ , and  $M$  is the mid-point of  $AC$ . Take a point  $P$  on the line segment  $BM$  such that  $\angle PAM=\angle MBA$ . If we have  $\angle BAP=41^{\circ}$  and  $\angle PDB=115^{\circ}$ , find the  $\angle BAC$ . 

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