
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]


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Suppose \(a, b,\) and \(c\) are nonnegative real numbers such that the sum of their squares is 52 and the sum of their pairwise products is 28. What is the maximum possible value of \(a+b+c\)?

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