
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 determinant of the matrix given by
\[\begin{vmatrix} a + 2c & b + 2d \\ c & d \end{vmatrix},\]
if it is known that \(\begin{vmatrix} a & b \\ c & d \end{vmatrix} = 7.\)

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