
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 $g(x) = \frac{2 - x}{1 + 2x}$, $g_1(x) = g(g(x))$, $g_2(x) = g(g_1(x))$, and in general $g_n(x) = g(g_{n-1}(x))$. What is the value of $g_{1989}(5)$?

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