
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 circle is inscribed in a right triangle \( ABC (\angle C = 90^\circ) \), touching its sides at points \( A_1, B_1, C_1 \). Find the ratio of the area of triangle \( ABC \) to the area of triangle \( A_1 B_1 C_1 \), given that \( AC = 4 \text{ cm} \) and \( BC = 3 \text{ cm} \).

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