
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
\[ f(x) = \sqrt{x(100 - x)} + \sqrt{x(4 - x)} \]
for \( 0 \le x \le 4 \). Find the maximum value \( M \) of \( f(x) \), and determine the value \( x = x_0 \) at which this maximum occurs. Enter the ordered pair \( (x_0, M) \).

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