
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
A binary sequence is a sequence in which each term is equal to  $0$  or  $1$ . A binary sequence is called  $\text{friendly}$  if each term is adjacent to at least on term that is equal to  $1$ . For example , the sequence  $0,1,1,0,0,1,1,1$  is  $\text{friendly}$ . Let  $F_{n}$  denote the number of  $\text{friendly}$  binary sequences with  $n$  terms. Find the smallest positive integer  $n\ge 2$  such that  $F_{n}>100$ 

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