
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
(a) A given number should be divided into two parts such that the sum, which is composed of the quotient of the first and second parts and the reciprocal of this quotient, is minimized.

(b) A given number should be divided into two parts such that the sum of the square roots of the parts is maximized.

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