
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
Someone used the table of cube numbers of natural numbers to calculate the square root. They calculated the square of 2.5 according to the following scheme. Let's determine the procedure's scheme and whether it is generally valid.

Given:
\[ 3.5^3 = 42.875 \]
\[ 1.5^3 = 3.375 \]

The difference:
\[ d = 39.5 \]

\( d - 2 = 37.5 \)

One-sixth of this is:
\[ \frac{1}{6} \times 37.5 = 6.25 = 2.5^2 \]

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