
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
Consider a list of integers [3, 7, 2, 7, 5, 2, x]. If the mean, median, and mode of this list are written in increasing order, they also form an arithmetic progression. Find the sum of possible values of x.

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