
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
According to the new college entrance examination rules in Zhejiang Province, each student needs to choose three elective subjects from seven elective subjects at the end of the first semester of high school. A student has already chosen physics and chemistry, and needs to choose one more subject from biology and technology in the science subjects, and one subject from political science, history, and geography in the humanities subjects. Let $E=$"choose biology", $F=$"choose a science subject", $G=$"choose political science", $H=$"choose a humanities subject". Four conclusions are given as follows:<br/>① $G$ and $H$ are mutually exclusive events but not complementary events, ② $F$ and $H$ are mutually exclusive and complementary events, ③ $P\left(F\right)+P\left(G\right)=1$, ④ $P\left(E\cup H\right)=P\left(E\right)+P\left(H\right)$.<br/>The correct numbers of the conclusions are ______. (Please write down the numbers of the conclusions you think are correct).

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