
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
Alice and Bob play a similar game with a basketball. On each turn, if Alice has the basketball, there is a 5/8 chance that she will toss it to Bob and a 3/8 chance that she will keep the basketball. If Bob has the basketball, there is a 1/4 chance that he will toss it to Alice, and if he doesn't toss it to Alice, he keeps it. Alice starts with the basketball. What is the probability that Alice has the basketball again after two turns?

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