
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 cards numbered 1 through 12. Each number on the card indicates his starting point on the number line. He will then spin the fair spinner, which has four congruent sectors with labels "move 1 space right" (twice), "move 1 space left," and "move 2 spaces right." After following the instruction indicated by his first spin, he will spin the spinner again and follow these new instructions. What is the probability that he ends up on a multiple of 4? Express your answer as a common fraction.

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