
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 ratio of the volume of two cubes is $\frac{1232}{405}$. To find the ratio of their side lengths in the form $\frac{a\sqrt{b}}{c\sqrt{d}}$, where $a$, $b$, $c$, and $d$ are integers, what is the value of $a+b+c+d$?

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