
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
\[ g(x) = \sqrt{x(100 - x)} + \sqrt{x(10 - x)} \]
for \(0 \le x \le 10\). Let \(N\) be the maximum value of \(g(x)\), and let \(x = x_1\) be the point where the maximum value is attained. Find the ordered pair \((x_1, N)\).

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