
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
For any real numbers \( x, y, z \), define the operation " \( * \) " as:
\[ x * y = \frac{3 x^{3} y + 3 x^{2} y^{2} + x y^{3} + 45}{(x + 1)^{3} + (y + 1)^{3} - 60} \]
and \( x * y * z = (x * y) * z \).
What is the value of \( 2021 * 2020 * 2019 * \cdots * 3 * 2 \)?

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