
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
 $AD$  and  $BC$  are both perpendicular to  $AB$ , and  $CD$  is perpendicular to  $AC$ . If  $AB = 4$  and  $BC = 3$ , find  $CD$ .

![Image](https://cdn.artofproblemsolving.com/attachments/1/9/209433735d993b0d414f449d314abba3d4b90a.png)

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