
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 smallest four two-digit primes are written in different squares of a \(2 \times 2\) table. The sums of the numbers in each row and column are calculated. Two of these sums are 24 and 28. The other two sums are \(c\) and \(d\), where \(c<d\). What is the value of \(5c + 7d\)?

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