
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 a group of children, their total age sums up to 50 years. The oldest one is 13 years old, another one is 10 years old. Except for the 10-year-old child, the ages of the remaining children form an arithmetic sequence with integer values. How many children are there, and how old is each child?

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