
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
Shooters A, B, and C have probabilities of hitting a target of $\frac {1}{2}$, a, and a respectively (where $0 < a < 1$). Each shooter shoots once, and the number of targets hit is denoted by $\xi$. Among the probabilities $P(\xi=i)$ (for i=0, 1, 2, 3), if the value of $P(\xi=1)$ is the greatest, then the range of values for the real number a is _______.

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