
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
Suppose $a,$ $b,$ and $c$ are three positive numbers such that $abc = 1,$ $a + \frac {1}{c} = 7,$ and $b + \frac {1}{a} = 12.$ Find $c + \frac {1}{b}.$

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