
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 algebraic cofactor of the element 7 in the third-order determinant $$\begin{vmatrix} \left.\begin{matrix}3 & 7 & 4 \\ x+a & 5 & 2 \\ 1 & 0 & x\end{matrix}\right.\end{vmatrix}$$ and denote it as $f(x)$. If the solution set of the inequality $f(x) > 0$ is $(-1, b)$, then find the value of the real number $a+b$.

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