
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
In a region, there are three settlements A, B, and C connected by country roads. Each pair of settlements is connected by several (more than one) roads. The roads are bidirectional. A route between two settlements is defined as either a direct road connecting them or a chain of two roads passing through the third settlement. It is known that there are 34 routes connecting settlements A and B, and 29 routes connecting settlements B and C. What is the minimum number of routes that can connect settlements A and C?

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