
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
In a certain factory in 2015, the daily cost $C$ (in ten thousand yuan) of producing a certain product and the daily output $x$ (in tons) satisfy the functional relationship $C=x+5$. The daily sales revenue $S$ (in ten thousand yuan) and the daily output $x$ have the functional relationship: $S=\begin{cases} 3x+\frac{k}{x-8}+7, & 0<x<6 \\ 16, & x\geqslant 6 \end{cases}$. It is known that the daily profit $L=S-C$. When $x=2$, $L=3$.

1. Find the value of $k$;
2. Find the daily output (in tons) when the daily profit can reach the maximum, and find the maximum value.

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