
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
If  $-1 < x < 1$  and  $-1 < y < 1$ , define the "relativistic sum''  $x \oplus y$  to be
\[
  x \oplus y = \frac{x + y}{1 + xy} \, .
\]
The operation  $\oplus$  is commutative and associative.  Let  $v$  be the number
\[
  v = \frac{\sqrt[7]{17} - 1}{\sqrt[7]{17} + 1} \, .
\]
What is the value of 
\[
  v \oplus v \oplus v \oplus v \oplus v 
  \oplus v \oplus v \oplus v \oplus v \oplus v 
  \oplus v \oplus v \oplus v \oplus v \, ?
\]
(In this expression,  $\oplus$  appears 13 times.)

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