
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, each with an integer age. One of them is 10 years old. If the oldest is 13 years old and the total sum of all their ages is 50, and if excluding the 10-year-old child the remaining children's ages form an arithmetic sequence in ascending order, how many children are in the group?

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