
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
If a marksman hits the target with probability $P$ ($0<P<1$) every time he shoots, and the outcomes of each shot are independent, the probability of "exactly 3 hits in 8 consecutive shots" is $\frac{1}{25}$ times the probability of "exactly 5 hits in 8 consecutive shots", find the value of $P$.

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