
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
Find the length of $PQ$ in the triangle below where $RP = 12$ and $\angle QPR = 45^\circ$.

[asy]
unitsize(0.5inch);
pair P, Q, R;
P = (0,0);
Q = (sqrt(6), sqrt(6));
R = (0,1);
draw(P--Q--R--P);
label("$P$", P, SW);
label("$Q$", Q, NE);
label("$R$", R, NW);
label("$12$", midpoint(P--R), W);
label("$45^\circ$", (0.4, -0.2), NE);
[/asy]

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