
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 or overlapping vertically are the same color? The tessellation consists of a base layer of rectangles uniformly placed and a top layer consisting of circles, where each circle overlaps four rectangles (one on each side, without side sharing).

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