
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 factory produces a certain product, with the daily cost $C$ (in ten thousand yuan) and daily production $x$ (in tons) satisfying the functional relationship $C=3+x$. The daily sales revenue $S$ (in ten thousand yuan) and daily production $x$ have the functional relationship $S= \begin{cases} \overset{3x+ \frac {k}{x-8}+5\;\;\;\;\;(0 < x < 6)}{14\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(x\geqslant 6)}\end{cases}$. The daily profit $L=S-C$. When $x=2$, $L=3$.
(1) Find the value of $k$;
(2) Find the daily production quantity that maximizes daily profit and determine the maximum value.

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