
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 a number line. He then spins a fair spinner shown below (with four equal sectors) and follows the instruction indicated by his spin. From this new point, he spins the spinner again and follows the resulting instruction. The spinner has the following instructions: move 2 spaces left, move 1 space left, move 1 space right, and stay at the current position. What is the probability that Jeff ends up at 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