
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
The flea Kuzya can make jumps along the line $L$. The starting point for jumps is point $A$ on line $L$. The length of each jump is $h$ and the direction of each jump is chosen randomly and equally likely. Find the probability that, after making between three and nine random jumps, Kuzya will be at a distance of $4h$ from $A$ at least once.

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