
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

An archipelago consisting of an infinite number of islands stretches along the southern shore of a boundless sea. The islands are connected by an infinite chain of bridges, with each island connected to the shore by a bridge. In the event of a severe earthquake, each bridge independently has a probability $p=0.5$ of being destroyed. What is the probability that after the severe earthquake, it will be possible to travel from the first island to the shore using the remaining intact bridges?

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