
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
Determine the constant $d$ such that
$$\left(3x^3 - 2x^2 + x - \frac{5}{4}\right)(ex^3 + dx^2 + cx + f) = 9x^6 - 5x^5 - x^4 + 20x^3 - \frac{25}{4}x^2 + \frac{15}{4}x - \frac{5}{2}$$

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