
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
In the triangle \(ABC\), another triangle \(A_1B_1C_1\) is inscribed and a third triangle \(A_2B_2C_2\) is circumscribed such that \(A_1B_1 \parallel A_2B_2\), \(A_1C_1 \parallel A_2C_2\), and \(B_1C_1 \parallel B_2C_2\). The area of triangle \(A_1B_1C_1\) is \(t_1\), and the area of triangle \(A_2B_2C_2\) is \(t_2\). What is the area of the triangle \(ABC\)?

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