
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
Let the sum of the first n terms of the sequence {a_n} be S_n. Determine the number of true propositions among the following:  
If the sequence {a_n} is both an arithmetic sequence and a geometric sequence, then a_n = a_{n+1};  
If S_n = an^2 + bn (a, b ∈ ℚ), then the sequence {a_n} is an arithmetic sequence;  
If S_n = 1 - (-1)^n, then the sequence {a_n} is a geometric sequence.

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