
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 minimum number of colors needed to shade the tessellation shown, such that no two adjacent tiles (tiles sharing a side) are the same color, if the tessellation consists of alternating squares and equilateral triangles?

[asy]
pair A=(0,0), B=(1,0), C=(0.5, sqrt(3)/2);
pair D=(1.5, sqrt(3)/2), E=(2,0), F=(2.5, sqrt(3)/2);
draw(A--B--C--cycle);
draw(B--D--C--cycle);
draw(B--E--D--cycle);
draw(E--F--D--cycle);
draw(shift((2,0))*(A--B--C--cycle));
draw(shift((2,0))*(B--D--C--cycle));
draw(shift((2,0))*(B--E--D--cycle));
draw(shift((2,0))*(E--F--D--cycle));
[/asy]

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