
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 type of instrument. Due to limitations in production capacity and technical level, some defective products are produced. According to experience, the defect rate $p$ of the factory producing this instrument is generally related to the daily output $x$ (pieces) as follows: 
$$
P= \begin{cases} 
\frac {1}{96-x} & (1\leq x\leq 94, x\in \mathbb{N}) \\ 
\frac {2}{3} & (x>94, x\in \mathbb{N})
\end{cases}
$$
It is known that for every qualified instrument produced, a profit of $A$ yuan can be made, but for every defective product produced, a loss of $\frac {A}{2}$ yuan will be incurred. The factory wishes to determine an appropriate daily output.
(1) Determine whether producing this instrument can be profitable when the daily output (pieces) exceeds 94 pieces, and explain the reason;
(2) When the daily output $x$ pieces does not exceed 94 pieces, try to express the daily profit $T$ (yuan) of producing this instrument as a function of the daily output $x$ (pieces);
(3) To obtain the maximum profit, how many pieces should the daily output $x$ be?

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