
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 maximum number of integers greater than 20 in a set of seven integers, given that the sum of all seven integers is 10 and at least two integers are less than -5, can be found by simplifying the problem and solving the inequality. First, let a be the number of integers greater than 20, let b be the number of integers equal to 0, and let c be the number of integers less than -5. Then the total sum can be rewritten as $20a+0b-5c$. Using the constraint of the total sum and the condition that c >= 2, we can form an inequality with two variables to find the maximum possible value for a.

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