
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
The areas of two triangles sharing a common altitude are 800 square feet and 1200 square feet respectively. If the length of the bases of these triangles are 40 feet and 60 feet respectively, find the common altitude.

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