
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 mathematical pendulum is suspended near a vertical wall and oscillates in a plane parallel to the wall. A thin nail is driven into the wall so that the middle of the pendulum's string strikes it each time the pendulum passes through the equilibrium position from right to left. Find the period of oscillation of the pendulum if the length of its string is $l = 2\, \text{m}$. The acceleration due to gravity is $g = 10\, \text{m/s}^2$.

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