
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 is a group of children whose total age is 50 years. The oldest is 13 years old, and one of them is 10 years old. Excluding the 10-year-old child, the ages of the remaining children form an arithmetic sequence. How many children are there, and what are their ages?

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