
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
Six resistors with resistances \( R_{1}=1 \) Ohm, \( R_{2}=2 \) Ohm, \( R_{3}=3 \) Ohm, \( R_{4}=4 \) Ohm, \( R_{5}=5 \) Ohm, and \( R_{6}=6 \) Ohm are connected in series and form a closed loop. A direct voltage source with voltage \( U=12 \) V is connected to this circuit in such a way that the resistance of the circuit between its terminals is maximized. Find the power \( P_{3} \) dissipated on the resistor \( R_{3} \).

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