
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
Before a total solar eclipse, calculations showed that at 9:13 AM, the distance between the centers of the sun and moon discs was $4 \frac{7}{10}$ lunar diameters. Both discs had the same apparent size and appeared to be moving in the same direction, from west to east. The moon moved $1 \frac{1}{16}$ lunar diameters per hour along its orbit, while the sun moved only $\frac{1}{12}$ of a lunar diameter in the same time.

a) At what time did the centers of the two discs coincide (total eclipse)?

b) When did the eclipse begin and

c) when did the eclipse end?

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