
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 daily life, specific times are usually expressed using the 24-hour clock system. There are a total of 24 time zones globally, with adjacent time zones differing by 1 hour. With the Prime Meridian located in Greenwich, England as the reference point, in areas east of Greenwich, the time difference is marked with a "+", while in areas west of Greenwich, the time difference is marked with a "-". The table below shows the time differences of various cities with respect to Greenwich:

| City   | Beijing | New York | Sydney | Moscow |
|--------|---------|----------|--------|--------|
| Time Difference with Greenwich (hours) | +8 | -4 | +11 | +3 |

For example, when it is 12:00 in Greenwich, it is 20:00 in Beijing and 15:00 in Moscow.

$(1)$ What is the time difference between Beijing and New York?
$(2)$ If Xiao Ming in Sydney calls Xiao Liang in New York at 21:00, what time is it in New York?
$(3)$ Xiao Ming takes a direct flight from Beijing to Sydney at 23:00 on October 27th. After 12 hours, he arrives. What is the local time in Sydney when he arrives?
$(4)$ Xiao Hong went on a study tour to Moscow. After arriving in Moscow, he calls his father in Beijing at an exact hour. At that moment, his father's time in Beijing is exactly twice his time in Moscow. What is the specific time in Beijing when the call is connected?

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