
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 $\lfloor x \rfloor$ denote the greatest integer less than or equal to $x$, for example, $\lfloor 1.7 \rfloor = 1$, $\lfloor 0.25 \rfloor = 0$, $\lfloor -3.4 \rfloor = -4$. Then, find the number of natural numbers $x$ that satisfy $\lfloor 3.8x \rfloor = \lfloor 3.8 \rfloor x + 1$.

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