
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 a set of data $2$, $9$, $6$, $10$, $x$, where the mode is $x$, and $x$ is an integer solution of the inequality system $\left\{\begin{array}{l}{2021x-4042>0}\\{14-2(x-3)>0}\end{array}\right.$, then the median of this set of data is ______.

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