
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
The sequence \(\left\{a_{k}\right\}\) is defined as: \(a_{1} = 1\), \(a_{2} = 1\), and \(a_{k} = a_{k-1} + a_{k-2}\) for \(k > 2\). If \(a_{1} + a_{2} + \ldots + a_{10} = 11a_{b}\), find the value of \(b\).

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