
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 $\angle PQR = 90^\circ$, what is the measure of $\angle PMN$? 
```asy
size(6cm);

pair p = (0, 0); 
pair m = dir(180 - 45); 
pair n = dir(180 + 45); 
pair r = 1.3 * dir(45); 
pair q = 1.3 * dir(-45);

label("$M$", m, SW); 
label("$R$", r, NE); 
label("$P$", p, 2*S); 
label("$N$", n, SE); 
label("$Q$", q, SE);

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

circle(p, 1.3);

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

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