
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 classic ancient Chinese mathematical work "The Mathematical Classic of Sunzi" recorded a problem as follows: "There is a certain number of objects unknown. When divided by $3$, there is a remainder of $2$; when divided by $5$, there is a remainder of $3$. How many objects are there?" Now, from the integers $1$ to $200$, a total of $200$ integers, the numbers that simultaneously satisfy "a remainder of $2$ when divided by $3$ and a remainder of $3$ when divided by $5" are arranged in ascending order to form a sequence $\{a_{n}\}$. The sum of the largest and smallest terms of this sequence is ______.

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