
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 $a$ is a nonzero integer and $b$ is a positive number such that $ab^3=\log_{10} b$, what is the median of the set $\{0, a, b, 1/b, ab\}$?

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