
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 $ABC$, point $D$ on $AB$ bisects angle $C$, and the lengths $BD$, $BC$, and $CD$ are provided. Find the length $AD$.
Given:
- $BD = 21$ cm,
- $BC = 30$ cm,
- $CD = 15$ cm.

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