
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 seven positive integers from a list of eleven positive integers are \(3, 5, 6, 9, 10, 4, 7\). What is the largest possible value of the median of this list of eleven positive integers if no additional number in the list can exceed 10?

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