
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
Jessica has a palette of three colors this time and a 3 by 3 grid to color. Each square in the grid that shares a side with another square cannot have the same color as any of its adjacent squares. How many distinct ways can Jessica color the grid?

[asy]
size(101);
for (int i = 1; i < 3; ++i) {
    draw((0, i/3) -- (1, i/3));
    draw((i/3, 0) -- (i/3, 1));
}
label("$A$",(0,1),NW); label("$B$",(0.33,1),N); label("$C$",(0.66,1),N); label("$D$",(1,1),NE);
label("$E$",(0,0.66),W); label("$F$",(0.33,0.66),N); label("$G$",(0.66,0.66),N); label("$H$",(1,0.66),E);
label("$I$",(0,0.33),W); label("$J$",(0.33,0.33),N); label("$K$",(0.66,0.33),N); label("$L$",(1,0.33),E);
label("$M$",(0,0),SW); label("$N$",(0.33,0),S); label("$O$",(0.66,0),S); label("$P$",(1,0),SE);
[/asy]

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