
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 components for an instrument. Due to limitations in production capacity and technical level, some defective products are produced. Based on experience, the defect rate $P$ is generally related to the daily output $x$ (in ten thousand units) as follows: 
$$
P= \begin{cases} \dfrac {1}{6-x} & (1\leqslant x < 6) \\ \dfrac {2}{3} & (x\geqslant 6) \end{cases}.
$$
Note: The defect rate $P$ = number of defective products / production volume. For example, $P=0.1$ means that for every 10 products produced, 1 is defective and the rest are qualified. It is known that for every ten thousand qualified components produced, a profit of 20,000 yuan can be made, but for every ten thousand defective products produced, a loss of 10,000 yuan will be incurred. Therefore, the factory wishes to determine the appropriate daily output.
1. Try to express the daily profit $T$ (in ten thousand yuan) as a function of the daily output $x$ (in ten thousand units);
2. What should the daily output $x$ be to maximize profit?

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