
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

On the planet Zilot, the units of measurement are quite different from those we know on Earth. The standard measure of length is the Zimeter, and one of its submultiples is the Zimimimeter, which is equivalent to $10^{-7}$ Zimeters. A calculator can perform only two operations: multiply a number by $10^{8}$ or divide it by $10^{5}$. For example, using the calculator's operations, we can make the following conversions:

$$
3 \rightarrow 3 \cdot 10^{-5} \rightarrow 3 \cdot 10^{-10} \rightarrow 3 \cdot 10^{-2}
$$

a) Explain how we can combine the two operations of the calculator to convert $7 \cdot 10^{2}$ Zimeters into Zimimimeters.

b) How do we obtain the conversion of $10^{10} \cdot 10^{-4}$ Zimeters into Zimimimeters starting with the number 1000 on the calculator's screen?

c) Using the calculator, is it possible to transform $10^{2017}$ into $10^{11}$ using the two mentioned buttons?

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