
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
Let
\[f(x) = \sqrt{x(75 - x)} + \sqrt{x(3 - x)}\]
for \(0 \le x \le 3.\) Let \(M\) be the maximum value of \(f(x),\) and let \(x = x_0\) be the point where the maximum value is attained. Determine the ordered pair \((x_0, M).\)

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