
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
Given the determinant \\( \begin{vmatrix} 1 & 2 & 4 \\\\ \\cos (π+x) & 2 & 0 \\\\ -1 & 1 & 6\\end{vmatrix} \\), if the value of the algebraic cofactor of the element \\(4\\) is equal to \\( \\dfrac {3}{2}\\), then the set of real number values for \\(x\\) is \_\_\_\_\_\_.

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