
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  $A_1=0$  and  $A_2=1$ .  For  $n>2$ , the number  $A_n$  is defined by concatenating the decimal expansions of  $A_{n-1}$  and  $A_{n-2}$  from left to right.  For example  $A_3=A_2A_1=10$ ,  $A_4=A_3A_2=101$ ,  $A_5=A_4A_3=10110$ , and so forth.  Determine all  $n$  such that  $11$  divides  $A_n$ .

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