
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
Which points in a right-angle coordinate system have $x, y$ coordinates that satisfy the equation

$$
\left[x-3\left[\frac{x}{3}\right]\right]+\left[y-3\left[\frac{y}{3}\right]\right]=a
$$

where I. $a=3$, and II. $a=2$? (The square brackets denote the integer part of the number, that is, $[x]$ is the integer such that

$$
[x] \leq x < [x]+1
$$



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