
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
Given a prime number $p = 11$, we want to know if integers $a$ within the set $\{1, 2, 3, ..., 10\}$ are primitive roots modulo $11$. A number $a$ is a primitive root modulo $11$ if $\{a^1, a^2, a^3, ..., a^{10}\}$ contains exactly one element congruent to each of $1, 2, 3, ..., 10 \pmod{11}$. Determine the sum of all integers in the set that are primitive roots modulo $11$.

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