
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
Four boys, \( A, B, C, \) and \( D \) made three statements each about the same number \( x \). We know that each of them has at least one statement that is true, but also at least one statement that is false. Determine whether \( x \) can be identified. The statements are:

\( A \):

1. The reciprocal of \( x \) is not less than 1.
2. The decimal representation of \( x \) does not contain the digit 6.
3. The cube of \( x \) is less than 221.

\( B \):

4. \( x \) is an even number.
5. \( x \) is a prime number.
6. \( x \) is an integer multiple of 5.

\( C \):

7. \( x \) cannot be expressed as a ratio of two integers.
8. \( x \) is less than 6.
9. \( x \) is a square of a natural number.

\( D \):

10. \( x \) is greater than 20.
11. \( x \) is positive, and its base-10 logarithm is at least 2.
12. \( x \) is not less than 10.

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