
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
Eleven positive integers from a list include $5, 6, 7, 2, 4, 8, 3$. What is the largest possible value of the median of this list of eleven positive integers if one of the remaining numbers must be at least 10?

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