
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
What is the least number of colors needed to shade the tessellation shown, such that no two tiles sharing a side are the same color? The tessellation includes interlocking hexagons and squares as depicted below:

[asy]
unitsize(1cm);
int i;
for(i=0; i < 7; i = i + 2){
    draw(shift(2*i,0)*polygon(6));
    draw(shift(2*(i+1), 0)*scale(0.577)*polygon(4));
}
[/asy]

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