
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 that $f'(x)$ is the derivative of the function $f(x)$, and for any real number $x$, we have $f'(x)=e^{x}(2x+3)+f(x)$ (where $e$ is the base of the natural logarithm), and $f(0)=1$. Determine the range of the real number $k$ such that the solution set of the inequality $f(x)-k < 0$ contains exactly two integers.

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