
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
In a tessellation consisting of rows of trapezoids and triangles alternately, what is the least number of colors needed to shade the tessellation such that no two tiles sharing a side are the same color?

[asy]
size(12cm,3cm);
for(int i = -8; i < 8; ++i) {
    draw((2*i,0)--(2*i+1,2)--(2*i+2,0)--cycle);
    draw((2*i,0)--(2*i+1,-2)--(2*i+2,0)--cycle);
}
[/asy]

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