
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
Consider a 3x3 grid where Jessica can use three different colors. If non-overlapping regions that share a side cannot be the same color, how many possible ways are there for Jessica to color the grid?

[asy]
size(151);
draw((0,0)--(0,1)--(1,1)--(1,0)--cycle);
draw((1,0)--(1,1)--(2,1)--(2,0)--cycle);
draw((2,0)--(2,1)--(3,1)--(3,0)--cycle);
draw((0,1)--(0,2)--(1,2)--(1,1)--cycle);
draw((1,1)--(1,2)--(2,2)--(2,1)--cycle);
draw((2,1)--(2,2)--(3,2)--(3,1)--cycle);
draw((0,2)--(0,3)--(1,3)--(1,2)--cycle);
draw((1,2)--(1,3)--(2,3)--(2,2)--cycle);
draw((2,2)--(2,3)--(3,3)--(3,2)--cycle);
label("$A$", (0.5, 2.5), N); label("$B$", (1.5, 2.5), N); label("$C$", (2.5, 2.5), N);
label("$D$", (0.5, 1.5), N); label("$E$", (1.5, 1.5), N); label("$F$", (2.5, 1.5), N);
label("$G$", (0.5, 0.5), N); label("$H$", (1.5, 0.5), N); label("$I$", (2.5, 0.5), N);
[/asy]

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