
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
If a subset \(B=\{0,1\}\) of the set \(A=\left\{\lg x, \lg y, \lg \left(x+\frac{y}{x}\right)\right\}\), find the largest possible value of the largest element of \(A\).

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