
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 sequence involving four 30-60-90 triangles starts with triangle ABC having hypotenuse AB = 12 cm. Each subsequent triangle has its longest leg as the hypotenuse for the next triangle’s longest leg. Calculate the area of the fourth triangle in the sequence.

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