
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
For a list of six positive integers, none greater than 100, the mean is twice the mode. If 21, 45, 77, $x$, $x$, and $y$ are the six integers, with $y > x$, what is the value of $x$?

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