
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
Jerry starts at 0 on the real number line. He tosses a fair coin 10 times. For each heads, he moves 1 unit in the positive direction; for each tails, he moves based on the previous toss outcome - if the previous was heads, he moves 1 unit in the negative direction, if the previous was tails, he moves 2 units in the negative direction. Calculate the probability that he reaches 3 at some time during this process.

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