
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
Calculate the value of the following determinant:

$$
\begin{aligned}
& a^{2}(a+1)^{2}(a+2)^{2}(a+3)^{2} \\
& b^{2}(b+1)^{2}(b+2)^{2}(b+3)^{2} \\
& c^{2}(c+1)^{2}(c+2)^{2}(c+3)^{2} \\
& \left|d^{2}(d+1)^{2}(d+2)^{2}(d+3)^{2}\right|
\end{aligned}
$$

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