
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 is a large square containing two smaller squares that can move freely within the large square (none of the smaller squares can move outside the large square, and their sides must be parallel to the sides of the large square). If the overlapping area of the two smaller squares ranges from a minimum of 9 to a maximum of 25, and the sum of the side lengths of the three squares (one large square and two smaller squares) is 23, then what is the sum of the areas of the three squares?

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