
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 \(\triangle ABC\), \(D\) and \(E\) are the midpoints of the sides \(AB\) and \(AC\) respectively. \(CD\) and \(BE\) intersect at \(P\) with \(\angle BPC = 90^\circ\). Suppose \(BD = 1829\) and \(CE = 1298\). Find \(BC\).

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