
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
Calculate the tax rate K using the formula $K=(1-7x)^{n}$ $(n\in\mathbb{N^{*}})$. Given that the sum of the binomial coefficients in the expanded form of K is 64, calculate the value of K when $x=\frac{3}{700}$ using the rounding method. If the value is accurate to 0.01, what is the digit in the hundredths place?

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