
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
A certain factory produces a product with a daily cost $C$ (unit: ten thousand yuan) related to the daily output $x$ (unit: tons) by the function $C = 3 + x$. The daily sales revenue $S$ (unit: ten thousand yuan) is related to the daily output $x$ by the function $S = \begin{cases}  3x + \frac{k}{x - 8} + 5, & \text{if } 0 < x < 6 \\ 14, & \text{if } x \geq 6 \end{cases}$. It is known that the daily profit $L = S - C$, and when $x = 2$, $L = 3$.
1. Find the value of $k$;
2. Determine the daily output in tons that maximizes the daily profit and calculate this maximum value.

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