
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
Consider the set  $E$  of all positive integers  $n$  such that when divided by  $9,10,11$  respectively, the remainders(in that order) are all  $>1$  and form a non constant geometric progression. If  $N$  is the largest element of  $E$ , find the sum of digits of  $E$ 

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