
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
Ten positive integers from a list include $5, 9, 3, 6, 10, 8$. What is the largest possible value of the median of this list of ten positive integers if all newly added integers must be consecutive starting from 11?

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