
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
\[ f(x) = \sqrt{x(40 - x)} + \sqrt{x(5 - x)} \]
for $0 \le x \le 5.$ Let $M$ be the maximum value of $f(x),$ and let $x = x_0$ be the point where the maximum value is attained. Find the ordered pair $(x_0, M)$.

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