
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
Altitudes \( \overline{AD} \) and \( \overline{BE} \) of an acute triangle \( \triangle ABC \) intersect at point \( H \). If \( HD = 8 \) and \( HE = 3 \), compute \( (BD)(DC) - (AE)(EC) \).

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