
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 $f(x) = \frac{x}{a(x+2)}$, and the equation $x = f(x)$ has a unique solution. Given that $f(x_0) = \frac{1}{1008}$ and $f(x_{n-1}) = x_n$ for $n=1, 2, 3, \ldots$, calculate $x_{2015}$.

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