
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 \(A, B, C, D, E, F, G, H\), depicted in a diagram. All channels are identical, and their connections occur at nodes denoted by \(B, D\), and \(G\). Water enters at node \(A\) and exits at node \(E\). Define the flow as the amount of cubic meters of water flowing through a channel cross-section per unit of time.

The farmer discovered that when moving through the channels from any point \(A, B, C, D, E, F, G\) or \(H\) to any other point, the sum of the flows is the same and does not depend on the path's shape (considering the sign, i.e., subtracting the flow if moving against the current).

It was found that the flow in channel \(A H\) equals \(q_{0}\). Find the flow in channel \(A B\), in channel \(B C\), and the total flow of water entering node \(A\).

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