
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
A farmer created an irrigation system of channels $A B C D E F G H$, as shown in the diagram. All channels are identical, and their connections occur at the nodes, labeled $B$, $D$, and $G$. Water enters at node $A$ and exits at node $E$. We define the flow rate as the number of cubic meters of water flowing through the cross-section of a channel per unit of time.

The farmer observed that when moving through the channels from any point $A, B, C, D, E, F, G,$ or $H$ to any other, the sum of the flow rates remains constant and does not depend on the path shape (taking signs into account; if moving against the flow, the flow rate is subtracted).

It was found that the total flow rate of water entering node $A$ is $q_{0}$. Find the flow rate in each of the channels $D E$, $BC$, and $G F$.

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