
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
There are 4 children and 2 coaches in the Chess Interest Group of Hongxing Primary School. The ages of the 4 children differ by 2 years sequentially, and the ages of the 2 coaches differ by 2 years. The sum of the squares of the ages of the 6 people is 2796 years. What is the sum of their ages in years?

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