
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 point $P(x+m,y+n)$, where $|x|\leqslant 3$, $|y|\lt\sqrt{17}$, $m^{2}+n^{2}\leqslant 1$, and $x$, $y$, $m$, $n$ are all integers. The possible positions of point $P$ in the Cartesian coordinate plane are ________.

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