
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
Volume  $ A$  equals one fourth of the sum of the volumes  $ B$  and  $ C$ , while volume  $ B$  equals one sixth of the sum of the volumes  $ C$  and  $ A$ .
Find the ratio of the volume  $ C$  to the sum of the volumes  $ A$  and  $ B$ .

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