
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
A gate is supported by two symmetrical metal plates shaped like isosceles triangles, as shown below. If $PQ = PR$ and $ST = SU,$ and the angles $\angle QPR = 40^\circ$ and $\angle TUS = 50^\circ,$ and a line is drawn perpendicular from $P$ to the midpoint $M$ of $ST$, calculate $\angle RPM + \angle MPT$.

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