
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 sides of lengths 40 units, 50 units, and 70 units. An altitude is dropped from the vertex opposite the side of length 70 units. Calculate the length of this altitude.
A) $\frac{40\sqrt{7}}{7}$ units
B) $\frac{80\sqrt{7}}{7}$ units
C) $\frac{120\sqrt{7}}{7}$ units
D) $\frac{160\sqrt{7}}{7}$ units

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