
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 the triangle  $ABC$ ,   $h_a, h_b, h_c$  are the altitudes   and  $p$  is its half-perimeter. Compare  $p^2$  with  $h_ah_b + h_bh_c + h_ch_a$ .

(Gregory Filippovsky)

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