
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 thin wooden rod is suspended by one end and can freely rotate around the suspension point. The lower end of the rod is immersed in water. At a certain immersion depth, the equilibrium position of the rod becomes unstable, and it starts deviating from the vertical position. Find this depth and the angle of the rod's deviation from the vertical as a function of immersion depth, given that the length of the rod is 1 meter, the density of its material is $0.6 \text{ kg/cm}^3$, and the density of water is $1 \text{ kg/cm}^3$.

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