
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 $\triangle ABC$, $\angle ABC=90^\circ$, $AB=5$ and $BC=12$. If perpendiculars are constructed to $\overline{AB}$ at $A$ and to $\overline{BC}$ at $C$ and they meet at point $D$, find the length of $CD$.

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