
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 structure consisting of a rigidly connected light rod and a small mass $m=1.6$ kg can oscillate under the action of two springs with stiffnesses $k_{1}=10 \frac{\mathrm{N}}{\mathrm{M}}$ and $k_{2}=7.5 \frac{\mathrm{N}}{\mathrm{M}}$, moving without friction around a vertical axis $O$ on a smooth horizontal table surface. The springs are light, their axes are horizontal, and the attachment points to the rod divide it into three equal parts. In the equilibrium position, the springs are not deformed. Find the period of small oscillations of the structure.

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