
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]


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A certain school laboratory has two potassium solutions with concentrations of 2g/ml and 0.2g/ml. Before use, the solutions need to be remixed. The operation method is to take 300ml each of the 2g/ml and 0.2g/ml K solutions and put them in two 500ml conical flasks A and B. First, take 100ml of the solution from flask A to flask B, mix thoroughly, then take 100ml of the solution from flask B to flask A and mix thoroughly again. One operation is completed after these two mixing processes. Assume that after completing the nth operation, the concentration of the solution in flask A is $a_n$ g/ml, and in flask B, it is $b_n$ g/ml. (Given $\lg 2 \approx 0.301$, $\lg 3 \approx 0.477$)

1. Calculate $a_1$, $b_1$, and determine whether the sequence $\{a_n - b_n\}$ is a geometric sequence. If it is, find its general formula. If not, explain why.
2. If the goal is to have the concentration difference between the solutions in flasks A and B to be less than $0.01$ g/ml, how many operations must be performed at minimum?

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