
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
Container $A$ contains 6 liters of saline solution with a concentration of $a\%$ salt, and container $B$ contains 4 liters of saline solution with a concentration of $b\%$ salt. One liter of the solution from $A$ is poured into $B$ and mixed, then one liter from $B$ is poured back into $A$. This process is repeated $k$ times (pouring from $A$ to $B$ and then from $B$ to $A$ counts as one repeat). After these $k$ repetitions, the concentrations of the saline solutions in containers $A$ and $B$ are $a_{k}\%$ and $b_{k}\%$ respectively.
(1) Find the sequence formed by $b_{k} - a_{k}$;
(2) Determine $a_{k}$ and $b_{k}$.

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