
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
Between Moscow and Saint Petersburg, there are seven settlements: Yaroslavl, Tver, Klin, Vyshny Volochek, Shestikhino, Zavidovo, and Bologoe. It is known that Moscow is connected by direct railway service to seven points, Saint Petersburg to five, Tver to four, Yaroslavl to two, Bologoe to two, Shestikhino to two, and Zavidovo to one. With how many settlements is Vyshny Volochek connected by direct service? In how many ways can one travel from Moscow to Saint Petersburg?

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