
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
Given Alice starts at 0 on the real number line, she rolls a fair six-sided dice 10 times. When she rolls a number from 1 to 3, she moves 1 unit in the positive direction; when she rolls 4 to 6, she moves 1 unit in the negative direction. What is the probability that she reaches exactly 3 units at some point during this process?

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