
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
In right triangle \(ABC\) (\(\angle C = 90^\circ \)), an altitude \(CD\) and a median \(CE\) are drawn. The areas of triangles \(ABC\) and \(CDE\) are 10 and 3, respectively. Find \(AB\).

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