
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
Jeff will pick a card at random from ten cards numbered 1 through 10. The number on this card will indicate his starting point on the number line shown below. He will then spin a newly designed fair spinner shown below (which has four congruent sectors) with the instructions: "move 1 space left", "move 1 space right", "move 1 space right", and "move 2 spaces right". From this new point, he will spin the spinner again and follow the resulting instruction. What is the probability that he ends up at a multiple of 3 on the number line?

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