
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
Among the following groups of vectors, which ones are collinear for vectors $a$ and $b$? Fill in the serial number.

$(1) a = - \dfrac{3}{2}e, b = 2e$ (where $e$ is a non-zero vector);

$(2) a = e_{1} - e_{2}, b = -3e_{1} + 3e_{2}$ (where $e_{1}, e_{2}$ are non-zero and not collinear vectors);

$(3) a = e_{1} - e_{2}, b = e_{1} + 2e_{2}$ (where $e_{1}, e_{2}$ are non-zero and not collinear vectors).

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