
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
Given an integer \( n \) (where \( n \geq 2 \)). For a \( 2n \)-element ordered array \( T = \left(a_1, b_1, a_2, b_2, \cdots, a_n, b_n \right) \), if each component of \( T \) is either 0 or 1, and for any \( p, q \) (where \( 1 \leq p < q \leq n \)), we have \( \left(a_p, b_p, b_q\right) \neq (1,0,1) \) and \( \left(a_q, b_q, a_p\right) \neq (1,0,0) \), then \( T \) is called an "interesting array". Find the number of interesting arrays.

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