
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
The angle \( A \) of the isosceles triangle \( \mathrm{ABC} \) measures \( \frac{2}{5} \) of a right angle, with angles \( B \) and \( C \) being equal. The bisector of angle \( C \) intersects the opposite side at point \( D \). Calculate the measures of the angles of triangle \( BCD \). Express the length \( a \) of side \( BC \) in terms of the length \( b \) of side \( AC \), without using trigonometric ratios in the expression.

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