
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
Which of the following statements are correct? (Fill in all the correct serial numbers)
① If $(1-x)^7 = a + a_1x + a_2x^2 + \dots + a_7x^7$, then $a_2 + a_4 + a_6 = 64$;
② The smallest term coefficient in the expansion of $(1-x)^7$ is the 5th term;
③ If we set $x = 100$, then dividing $(1-x)^7$ by $1000$, the remainder is 301;
④ The coefficient of the $x^5$ term in the expanded series of $(1-x) + (1-x)^2 + \dots + (1-x)^7$ is -28.

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