
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
Observe the following expressions, what pattern do you find? $1 \times 3 = 2^2 - 1$; $3 \times 5 = 4^2 - 1$; $5 \times 7 = 6^2 - 1$; $7 \times 9 = 8^2 - 1$; ...; Express the pattern you conjecture using an expression with only one letter: .

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