
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
The archipelago consists of several small islands and one large island. It was decided to build bridges between the islands so that the large island is connected to each small island by two bridges, and any two small islands are connected by one bridge.

By November 1st, all bridges between the small islands had been built, and a few (at least one) bridges leading to the large island had also been constructed, totaling 28 bridges in all. How many islands are there in total in the archipelago?

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