
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 $[x]$ denote the largest integer not greater than the real number $x$. The function $f(x)$ is defined as:

$$
f(x) =
\begin{cases}
\ln^2{x} - [ \ln{x} ] - 2, & \text{if } x > 2 \\
e^{-x} - ax - 1, & \text{if } x \leq 0
\end{cases}
$$

Determine the range of the real number $a$ such that $f(x)$ has exactly 5 zeros.

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