
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 the permutation $(a_1,a_2,\dots,a_{11})$ of the numbers $1,2,3,4,5,6,7,8,9,10,11$, determine the maximum number of $a_i$s that can be uniquely determined when we get $(a_1+a_3, a_2+a_4,a_3+a_5,\dots,a_8+a_{10},a_9+a_{11})$.

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