
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 is spread out along the southern shore of an endless sea in a chain. The islands are connected by an infinite chain of bridges, and each island is also connected to the shore by a bridge. In the event of a strong earthquake, each bridge independently has a probability $p=0.5$ of being destroyed. What is the probability that, after a strong earthquake, it will be possible to travel from the first island to the shore using the remaining bridges?

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