
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
Suppose that \( 0 < a < b < c < d = 2a \) and
$$
(d - a)\left(\frac{a^2}{b - a} + \frac{b^2}{c - b} + \frac{c^2}{d - c}\right) = (a + b + c)^2
$$

Find \( \frac{bcd}{a^3} \).

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