
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 structure consists of two weightless rods \(AB\) and \(CD\), a weightless pulley, and a load with mass \(m = 3\) kg, which is suspended at point \(G\). All cords are weightless and inextensible. The rod is connected to the hinge at point \(A\), which allows the rod to rotate within the plane of the drawing. The lengths are \(CG = \frac{1}{4} CD\) and \(AE = \frac{1}{4} AB\), and point \(F\) is the midpoint of rod \(AB\). The acceleration due to gravity is \(g = 10 \ \mathrm{m} / \mathrm{s}^2\). Determine the tension force \(T_{0}\) in the cord attached to rod \(AB\) at point \(E\).

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