
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
Given the function $f(x) = \left\lfloor \frac{x+1}{2} \right\rfloor - \left\lfloor \frac{x}{2} \right\rfloor$ where $x \in \mathbb{N}$, determine its range. (Note: $\left\lfloor x \right\rfloor$ represents the greatest integer not larger than $x$. For example, $\left\lfloor 3.15 \right\rfloor = 3$, $\left\lfloor 0.7 \right\rfloor = 0$.)

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