
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 $y \neq -1$. Define

$$
x_{1} = \frac{y-1}{y+1}, \quad x_{2} = \frac{x_{1}-1}{x_{1}+1}, \quad x_{3} = \frac{x_{2}-1}{x_{2}+1}, \ldots
$$

What is the value of $y$ if $x_{1978} = -\frac{1}{3}$?

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