
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 the diagram, if $\angle PQR = 60^\circ$, what is the measure of $\angle PMN$ assuming $MP$ extends to form an angle $\angle MPR = 20^\circ$? [asy]

size(6cm);

pair p = (0, 0); pair m = dir(180 - 20); pair n = dir(180 + 20); pair r = 1.5 * dir(20); pair q = 2 * 1.5 * Cos(60) * dir(-20);

label("$M$", m, N); label("$R$", r, N); label("$P$", p, 1.5 * S); label("$N$", n, S); label("$Q$", q, SE);

draw(m--p--r--m);
draw(n--p--q--n);

add(pathticks(m--p, s=4));
add(pathticks(n--p, s=4));
add(pathticks(r--p, 2, spacing=0.9, s=4));
add(pathticks(r--q, 2, spacing=0.9, s=4));

[/asy]

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