
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
For each integer \( n \geq 2 \), consider a regular polygon with \( 2n \) sides, all of length 1. Let \( C(n) \) denote the number of ways to tile this polygon using quadrilaterals whose sides all have length 1. Determine the limit inferior and the limit superior of the sequence defined by:
\[ 
\frac{1}{n^{2}} \log_{2} C(n) 
\]

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