
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 the sequence  $a_{1}, a_{2}, \cdots$  be defined recursively as follows:  $a_{n}=11a_{n-1}-n$ . If all terms of the sequence are positive, the smallest possible value of  $a_{1}$  can be written as  $\frac{m}{n}$ , where  $m$  and  $n$  are relatively prime positive integers. What is  $m+n$ ?

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