
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 a right  $\Delta ABC$  ( $\angle C = 90^{\circ} $ ),  $CD$  is the height. Let  $r_1$  and  $r_2$  be the radii of inscribed circles of  $\Delta ACD$  and  $\Delta DCB$ . Find the radius of inscribed circle of  $\Delta ABC$ 

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