
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
There are 11 positive numbers such that both their sum and the sum of their reciprocals equal 102. Let \(x\) be one of these numbers. Find the maximum value of \(x + \frac{1}{x}\).

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