
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
If \(a^{2} - 1 = 123 \times 125\) and \(a > 0\), find \(a\).

If the remainder of \(x^{3} - 16x^{2} - 9x + a\) when divided by \(x - 2\) is \(b\), find \(b\).

If an \(n\)-sided polygon has \((b + 4)\) diagonals, find \(n\).

If the points \((3, n), (5,1)\), and \((7, d)\) are collinear, find \(d\).

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