
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 $x \in \mathbb{R}$, and use $[x]$ to denote the greatest integer less than or equal to $x$ (for example, $[2.32]=2$, $[-4.76]=-5$). For a given $n \in \mathbb{N}^{*}$, define $C^{x}_{n} = \frac{n(n-1)\ldots(n-[x]+1)}{x(x-1)\ldots(x-[x]+1)}$, where $x \in [1,+\infty)$, then when $x \in [\frac{3}{2},3)$, the range of the function $f(x)=C^{x}_{10}$ is \_\_\_\_\_\_.

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