
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
Vasya has  $n{}$  candies of several types, where  $n>145$ . It is known that for any group of at least 145 candies, there is a type of candy which appears exactly 10 times. Find the largest possible value of  $n{}$ .

*Proposed by A. Antropov*

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