
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
A cafe has 3 tables and 5 individual counter seats. People enter in groups of size between 1 and 4, and groups never share a table. A group of more than 1 will always try to sit at a table, but will sit in counter seats if no tables are available. Conversely, a group of 1 will always try to sit at the counter first. One morning, \( M \) groups consisting of a total of \( N \) people enter and sit down. Then, a single person walks in and realizes that all the tables and counter seats are occupied by some person or group. What is the minimum possible value of \( M + N \)?

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