
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
Given the functions $f(x) = ax^2 - 2ax + a + 1$ ($a > 0$), and $g(x) = bx^3 - 2bx^2 + bx - \frac{4}{27}$ ($b > 1$), then the number of zeros of the function $y = g(f(x))$ is \_\_\_\_\_\_.

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