
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
Observe the following equations:  
$3^2 + 4^2 = 5^2$  
$10^2 + 11^2 + 12^2 = 13^2 + 14^2$  
$21^2 + 22^2 + 23^2 + 24^2 = 25^2 + 26^2 + 27^2$  
Then, the expression for the next equation is:

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