
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
Given a rhombus with side length 5, one of its diagonals is not greater than 6, and another is not less than 6, calculate the maximum value of the sum of the lengths of the two diagonals.

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