
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
Let $a$ and $b$ be real numbers such that:
\[a^3 - 12a^2 + 47a - 60 = 0\]
\[\text{and}\]
\[-b^3 + 12b^2 - 47b + 180 = 0.\]
Compute $2a - b.$

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