
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
Let the function \( \operatorname{lac}(x) \), defined on the set of real numbers, be given by the following rule:

$$
\operatorname{lac}(x) = 
\begin{cases}
x, & \text{if } x \in [2n, 2n+1], \text{ where } n \in \mathbb{Z} \\
-x + 4n + 3, & \text{if } x \in (2n+1, 2n+2), \text{ where } n \in \mathbb{Z}
\end{cases}
$$

Solve the equation \( \operatorname{lac}(2x^2 + x + 4) = \operatorname{lac}(x^2 + 7x - 1) \) in the set of real numbers.

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