
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
Let {a<sub>n</sub>} be an arithmetic sequence with a non-zero common difference, and $$a_{2}^{2}+a_{3}^{2}=a_{4}^{2}+a_{5}^{2}$$. Find the sum of the first 6 terms of {a<sub>n</sub>}.

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