
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 is going to pick a card randomly from twelve cards numbered 1 through 12.  The number on this card indicates his starting position on a number line. From there, he will spin a fair spinner divided into four equal sectors: one marked 'Move 2 spaces right', one marked 'Move 1 space right', and two marked 'Move 1 space left'. After moving according to the first spin's outcome, he will spin again and follow the new instruction. What is the probability that he will end up on a multiple of 3 on the number line? Express your answer as a common fraction.

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