
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:

$$
\left|\begin{array}{llll}
a_{1} & b_{1} & c_{1} & d_{1} \\
a_{1} & b_{2} & c_{2} & d_{2} \\
a_{1} & b_{2} & c_{3} & d_{3} \\
a_{1} & b_{2} & c_{3} & d_{4}
\end{array}\right|
$$

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