
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 right triangle $PQR$, with $\angle Q$ as the right angle, $\sin{R} = \frac{15\sqrt{34}}{34}$. Find the length of side $PQ$.

[asy]
draw((0,0)--(7,0)--(0,9)--cycle,black+linewidth(1));
draw(rightanglemark((7,0),(0,0),(0,9),20),black+linewidth(1));
label("$P$",(0,0),W);
label("$Q$",(7,0),E);
label("$R$",(0,9),W);
label("$\sqrt{34}$",(7,0)--(0,9),NE);
[/asy]

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