
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
Under the call for energy conservation, emission reduction, and protection of the Earth's environment, countries around the world attach great importance to the treatment of industrial wastewater and exhaust emissions. Despite the treatment of wastewater and exhaust gases by enterprises, it still poses some harm to the environment. Therefore, enterprises must pay a certain environmental compensation fee to local residents when discharging wastewater and exhaust gases. It is known that the environmental compensation fee $P$ paid by an enterprise is related to its wastewater discharge volume $x$ by the relationship $P=kx^3$ ($k\in[1,10]$), where the specific value of $k$ is determined by the local environmental protection department. The gross profit $Q$ of the enterprise satisfies the relationship $Q= \frac {1}{2}x^2+10x$,
(1) When $k=1$, what will be the wastewater discharge volume to maximize the net profit ($Q-P$) of the enterprise?
(2) When $x>1$, it will pose a risk to the health of residents. Within what range should the local environmental protection department set the value of $k$ to ensure that the enterprise does not pose a health risk to local residents when achieving maximum profit?

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