
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 certain type of artillery shell, after being fired, has its horizontal distance \\(x\\) from the launch point and its height \\(y\\) (in kilometers) above the ground satisfying the following relationship: \\(y=kx- \dfrac{{k}^{2}+1}{20} x^{2}\\), where \\(k\\) is an adjustment parameter related to the firing angle, and \\(k > 0\\).

\\((1)\\) Find the maximum range \\((\\)the horizontal distance between the landing point and the launch point\\()\\) of this type of artillery shell in kilometers.

\\((2)\\) If a certain flying object \\((\\)ignoring its size\\()\\) flies at a height of \\(3.2\\) kilometers, what is the maximum horizontal distance between the launch point and the flying object to ensure the artillery shell can hit it?

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