在
zài
在 is one pin stuck in the map
The picture A hand pushing a pin into a map. People, actions and even times all sit on that pin. 在 pins the action to the spot called now; 着 leaves the finished shape of it standing. 他在拿杯子 is picking the cup up right now, 他拿着杯子 is already holding it.
Where the picture shows up in 在
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a person on the pin
我在公司，你呢？
wǒ zài gōngsī, nǐ ne
I am at the office, where are you?
A pin goes into the office building on the map, and your own face sits on its head.
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a thing on the pin
钥匙在桌子上。
yàoshi zài zhuōzi shang
The keys are on the desk.
A pin goes into the exact spot on the desktop where the keys are lying.
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where the action happens
请在这里签名。
qǐng zài zhèlǐ qiānmíng
Please sign here.
A finger presses down on the blank line of the form and holds there: right here.
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the pin called now
他在打电话，等一下。
tā zài dǎ diànhuà, děng yíxià
He is on the phone, one moment.
Into the box marked now, the whole picture of him with the phone at his ear is pinned.
在 plus a verb is not separate grammar. It just pins the action to the spot called now.
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the pin on the clock
会议在下午两点开始。
huìyì zài xiàwǔ liǎng diǎn kāishǐ
The meeting starts at two in the afternoon.
A pin labelled meeting is pushed into the two o'clock mark on the clock face.
All of it in one picture
The pin in the office building carries a person; the pin on the desktop carries a set of keys. The finger pressed on the blank line marks where the act will happen, the phone call pinned into the box marked now sets an action on a moment, and the pin at two o'clock sets an appointment on a time. The gesture is identical all five times; only the map changes, from space to clock face. So do not memorise several meanings for 在, just see which map it was pinned to.