
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 
\[ g(x) = \sqrt{x(100 - x)} + \sqrt{x(8 - x)} \] for \(0 \leq x \leq 8\). Determine the maximum value of \(g(x)\) and the value of \(x\) where this maximum is attained. Let \(M\) be the maximum value and \(x = x_1\) be the point where it is reached. Enter the ordered pair \((x_1, M)\).

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