
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 function $f(x)$ defined as follows:
$$f(x) = \begin{cases} 2x+1, & x \in [-2, 2] \\ 1+x^{2}, & x \in [2, 4] \end{cases}$$
If $\int_{k}^{3} f(x) dx = \frac{40}{3}$, where $k < 2$, find the value of $k$.

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