
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
There are \( a_{1} \) students in a class who have received at least one failing grade over the year, \( a_{2} \) students who have received at least two failing grades, ..., \( a_{k} \) students who have received at least \( k \) failing grades. How many failing grades are there in total in this class?

(It is assumed that no student has received more than \( k \) failing grades.)

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