
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
When tossing two coins, if the probabilities of getting "two heads", "two tails", and "one head and one tail" are denoted as $P_1$, $P_2$, and $P_3$ respectively, then among the following judgments, the correct ones are \_\_\_\_\_\_. (Fill in the serial number)  
① $P_1 = P_2 = P_3$  
② $P_1 + P_2 = P_3$  
③ $P_1 + P_2 + P_3 = 1$  
④ $P_3 = 2P_1 = 2P_2$.

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