
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 \( k, \alpha \) and \( 10k - \alpha \) be positive integers. What is the remainder when the following number is divided by 11?

\[ 
8^{10k + \alpha} + 6^{10k - \alpha} - 7^{10k - \alpha} - 2^{10k + \alpha} 
\]

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