
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
Circle $\Omega$ is the incircle of $\triangle DEF$ and is also the circumcircle of $\triangle MNP$. The point $M$ is on $\overline{EF}$, the point $N$ is on $\overline{DF}$, and the point $P$ is on $\overline{DE}$. If $\angle D=50^\circ$, $\angle E=70^\circ$, and $\angle F=60^\circ$, what is the measure of $\angle MNP$?

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