
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
Construct the three altitudes of a given triangle with the minimum number of construction steps! Count a step as the drawing of a visible line: a circle, a circular arc, or a straight line; do not count the selection of the compass span, placing the compass point, or appropriately positioning the straightedge (even though these actions require attention, they are not visible).

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