
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 game involves tossing rings onto pegs. The player receives four rings and throws each of these rings until hitting a peg for the first time. The probability of hitting the peg with each throw is 0.1. Find the distribution series of the random variable $X$, which is the number of rings the player did not use.

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