
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 an isosceles right triangle \( ABC \), a segment \( BD \) equal to \( BC \) is laid on the extension of the hypotenuse \( AB \) beyond point \( B \), and point \( D \) is connected with \( C \). Find the sides of triangle \( ADC \) if the leg \( BC = a \).

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