
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
Walking slowly is a simple and excellent way to exercise, which can not only help with weight loss but also enhance cardiovascular function, vascular elasticity, muscle strength, etc. Xiao Nan plans to walk a certain number of kilometers each month for nearly 6 months. The distances (in kilometers) are arranged in ascending order as $11$, $12$, $m$, $n$, $20$, $27$, and the median of these 6 months' walking distances is $16$. If we want to minimize the standard deviation of these 6 months' walking distances, then $m=\_\_\_\_\_\_$.

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