
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 \( a = 1.8 \times 5.0865 + 1 - 0.0865 \times 1.8 \), find \( a \).

In the diagram shown, \( OH = OK = a \) units and \( OABC \) is a rectangle. \( AC = b \) units. What is \( b \)?

In the expression shown, what is \( c \) when it is expanded to the term with \( x^{(b-2)} \) as the numerator?

As shown, a rabbit spends \( c \) minutes in traveling from \( A \) to \( B \) along a half circle. With the same speed, it spends \( d \) minutes in traveling from \( A \rightarrow B \rightarrow D \) along half circles. What is \( d \)?

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