
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
Let  $n>1$  be a positive integer. Find the number of binary strings  $(a_1, a_2, \ldots, a_n)$ , such that the number of indices  $1\leq i \leq n-1$  such that  $a_i=a_{i+1}=0$  is equal to the number of indices  $1 \leq i \leq n-1$ , such that  $a_i=a_{i+1}=1$ .

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