
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
Given a rectangular box with dimensions $2 \times b \times c$, where $b$ and $c$ are integers with $b \leq c$, find the number of ordered pairs $(b, c)$ such that the sum of the volume and the surface area of the box equals 120.

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