
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 new tessellation shown, such that no two tiles sharing a side or a corner are the same color?

[asy]
draw((0,0)--(8,0)--(8,8)--(0,8)--cycle);
draw((2,0)--(2,8));
draw((6,0)--(6,8));
draw((0,2)--(8,2));
draw((0,6)--(8,6));
draw((2,2)--(6,6));
draw((6,2)--(2,6));
[/asy]

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