
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
\(\triangle ABC\) is equilateral with side length 4. \(D\) is a point on \(BC\) such that \(BD = 1\). If \(r\) and \(s\) are the radii of the inscribed circles of \(\triangle ADB\) and \(\triangle ADC\) respectively, find \(rs\).

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