Try to rewire Nest and Furnace but Y is not used on Furnace

I installed a Nest at home and it worked OK. Recently, I noticed there was a power issue. Google and others suggested adding a power supply by using the existing G wire because there are only 4 wires. Here is what I am planing to do:

On Nest side:

• disconnect current G wire (green) and connect it to the C terminal

On furnace side:

1. disconnect G wire(green) from the G terminal and connect it to the C
   terminal
2. Add a jumper wire between Y and G.

However, when I checked my furnace, there is no wire on Y terminal, and there is a blue wire which directly connected to C terminal. But on my Nest side, there is no blue wire, instead, there is a black wire which connected to Y1. If I follow the above step and rewire Green wire to C terminal, what is the next? I tried, if I rewire Green wire to C terminal, when I turned on the cooling, the fan was not on, but the condenser is running.

Please provide you suggestions.

For reference, the current connection on Nest side is:

• Black wire – > Y1;
• White wire – > W1;
• Red wire – > Rh;
• Green wire – > G;