
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
Let $\triangle ABC$ be a right-angled triangle with $m\angle BAC = 90^{\circ}$. Let $P$ and $Q$ be the midpoints of legs $AB$ and $AC$, respectively. Given that $QC=25$ and $PB=28$, find $BC$.

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