
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
On the sides of the acute angle $ABC$, points $A$ and $C$ are taken. One circle touches the line $AB$ at point $B$ and passes through point $C$. The second circle touches the line $BC$ at point $B$ and passes through point $A$. Point $D$ is the second common point of the circles. It is known that $AB = a$, $CD = b$, $BC = c$. Find $AD$.

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