
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 capacities of three containers $A$, $B$, and $C$, each of which is shaped like a cube, are in the ratio $1: 8: 27$, and the volumes of water initially filled in them are in the ratio $1:2:3$. After transferring some water from container $A$ to container $B$ and from container $B$ to container $C$, each container ended up with the same depth of water. Later, $128 \frac{4}{7}$ liters of water were transferred from container $C$ to container $B$, and subsequently, an amount of water was moved from container $B$ to container $A$ such that the depth of water in container $A$ became twice that in container $B$. It turned out that container $A$ now had $10 \theta$ liters less water than it initially had. How much water was initially in each container?

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