
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
Bridges. Along the southern shore of the endless sea stretches an archipelago of an infinite number of islands. The islands are connected by an infinite chain of bridges, and each island is connected by a bridge to the shore. In the event of a strong earthquake, each bridge independently has a probability of $p=0.5$ 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