
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
Given in $\triangle ABC$, $\angle C=90^\circ$, $AC=4$, $BC=3$, and $CD$ is the altitude from $C$ to $AB$. $O_1$ and $O_2$ are the incenters of $\triangle ACD$ and $\triangle BCD$ respectively. Then, the length of $O_1O_2$ is     .

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