
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
For watering his plot, a farmer created a system of channels \( A B C D E F G H \) depicted in a diagram. All channels are identical, and their connections occur at the nodes marked \( B, D, \) and \( G \). Water enters at node \( A \) and exits at node \( E \). The flow rate is defined as the number of cubic meters of water passing through a cross-section of a channel per unit time.

The farmer found that moving through channels from one point \( A, B, C, D, E, F, G, \) or \( H \) to any other, the total flow rate remains the same and does not depend on the path shape (considering the sign, if we move against the flow, the flow rate is subtracted).

It was determined that the flow rate in channel \( BC \) is \( q_{0} \). Find the flow rate in channel \( AB \), in channel \( AH \), and the total flow rate of water entering at node \( A \).

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