
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 side lengths of 9, 12, and 15 units. Calculate both the area of the triangle and the height from the right angle vertex to the hypotenuse.

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