
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 $\triangle ABC$, point $P$ is a moving point on segment $BC$. Points $R$ and $Q$ lie on sides $AB$ and $AC$ respectively, such that $PQ \parallel AB$ and $PR \parallel AC$. Let $AC = b$, $AB = c$, and $\angle BAC = \alpha$. Find the minimum length of $RQ$ (expressed in the simplest form using $b$, $c$, and $\alpha$).

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