
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
Quadrangle  $ ABCD$  is inscribed in a circle with radius 1 in such a way that the diagonal  $ AC$  is a diameter of the circle, while the other diagonal  $ BD$  is as long as  $ AB$ . The diagonals intersect at  $ P$ . It is known that the length of  $ PC$  is  $ 2/5$ . How long is the side  $ CD$ ?

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