
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
How do the results of the 1965 National Secondary School Mathematical Competition Round II, problem 1, change if the angle data is rounded to $0.1^{\circ}$, and—as usual—the rounded digit is taken as even if the discarded part is exactly half of the last retained digit's place value, meaning if

$$
11.35^{\circ} \leq \alpha \leq 11.45^{\circ}, \quad \text { and } \quad 4.65^{\circ} < \beta < 4.75^{\circ}
$$

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