
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 construction consisting of a rigidly connected lightweight rod and a small mass of $m=1$ kg can oscillate under the action of two springs with stiffnesses $k_{1}=60 \ \text{N/m}$ and $k_{2}=10 \ \text{N/m}$, moving frictionlessly around a vertical axis $O$ on a smooth horizontal surface of a table. The springs are lightweight, their axes are horizontal, and the points of attachment 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 construction.

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