
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
In the theory of concave mirrors, the following formula is encountered:

$$
x = r \frac{\sin^2 \frac{\alpha}{2}}{\cos x}
$$

For small $\alpha$, this formula approximates closely to $x = \frac{r \alpha^2}{4}$. Justify this approximation. In which units of measurement is the angle $\alpha$ expressed?

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