
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
a) Solve the system of equations  $\begin{cases}
1 - x_1x_2 = 0 
1 - x_2x_3 = 0 
...
1 - x_{14}x_{15} = 0 
1 - x_{15}x_1 = 0 \end{cases}$ b) Solve the system of equations  $\begin{cases}
1 - x_1x_2 = 0 
1 - x_2x_3 = 0 
...
1 - x_{n-1}x_{n} = 0 
1 - x_{n}x_1 = 0 \end{cases}$ How does the solution vary for distinct values of  $n$ ?

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