
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 $\angle PQR = 60^\circ$ and triangle $PMQ$ is isosceles with $PM = MQ$, what is the measure of $\angle PMN$? Assume that $\angle MPN$ and $\angle PQR$ are opposite angles, and $PR = RQ$.
[asy]
size(6cm);
pair p = (0, 0); pair m = dir(180 - 30); pair n = dir(180 + 30); pair r = 1.3 * dir(30); pair q = 2 * 1.3 * Cos(60) * dir(-30);
label("$M$", m, N); label("$R$", r, N); label("$P$", p, 1.5 * S); label("$N$", n, S); label("$Q$", q, SE);
draw(m--q--r--n--cycle);
add(pathticks(m--p, s=4));
add(pathticks(q--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}
user