
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 $\angle PQR = 60^\circ$, calculate the measure of $\angle PMN$, assuming $\triangle PMR$ is an isosceles triangle. Consider $\triangle RQN$ is also isosceles with $RQ = RN$. [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(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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