
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
If \( H \) is the orthocenter of triangle \( ABC \), then

\[ H A \cdot h_{a} + H B \cdot h_{b} + H C \cdot h_{c} = \frac{a^{2} + b^{2} + c^{2}}{2} \]

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