
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 \( S \) be the smallest subset of the integers with the property that \( 0 \in S \) and for any \( x \in S \), we have \( 3x \in S \) and \( 3x + 1 \in S \). Determine the number of non-negative integers in \( S \) less than 2008.

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