
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
Given a set of 7 numbers, with 4 of the numbers known as 10, 2, 5, and 4, and 1 number not clearly remembered, such that the mean, median, and mode of this set of numbers form an arithmetic sequence in that order, calculate the sum of all possible values of the missing number.

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