
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
1.1 Find \( a \) if \( a = \log_{5} \frac{(125)(625)}{25} \).

1.2 If \( \left(r + \frac{1}{r}\right)^{2} = a - 2 \) and \( r^{3} + \frac{1}{r^{3}} = b \), find \( b \).

1.3 If one root of the equation \( x^{3} + c x + 10 = b \) is 2, find \( c \).

1.4 Find \( d \) if \( 9^{d+2} = (6489 + c) + 9^{d} \).

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