
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
The Titius-Bode law, abbreviated as the "Bode law," is an empirical rule that represents the average distance between each planet and the sun. It was discovered by a German high school teacher, David Titius, in 1766. Later, it was summarized by the director of the Berlin Observatory, Bode, into an empirical formula as follows: Let the average distance from the sun to the Earth be $1$. If a planet is numbered as $n$, then the average distance from that planet to the sun is represented as $a + b \times 2^{n-1}$. Determine the average distance of the planet numbered $9$ according to this formula.

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