
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

Find all possible values of
$$
\left\lfloor\frac{x-p}{p}\right\rfloor+\left\lfloor\frac{-x-1}{p}\right\rfloor,
$$
where $x$ is a real number and $p$ is a nonzero integer. 

Here $\lfloor z\rfloor$ denotes the greatest integer less than or equal to $z$.

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