
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 \( A \) be a non-empty subset of the set of positive integers. If all sufficiently large positive integers can be expressed as the sum of two (not necessarily distinct) numbers from \( A \), then \( A \) is called a basis of order 2. For \( x \geqslant 1 \), let \( A(x) \) be the number of elements in \( A \) that are at most \( x \).

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