
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
A triangle has two medians of lengths 5 inches and 9 inches which are perpendicular to each other, and the area of the triangle is $6 \sqrt{35}$ square inches. Calculate the length of the third median.
A) $3\sqrt{7}$
B) $2\sqrt{7}$
C) $5\sqrt{7}$
D) $4\sqrt{7}$
E) $6\sqrt{7}$

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