
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 $\triangle PQR$, $\angle PQR = 150^\circ$, $PQ = 4$ and $QR = 6$. If perpendiculars are constructed to $\overline{PQ}$ at $P$ and to $\overline{QR}$ at $R$, and they meet at point $S$, calculate the length of $RS$.

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