
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
Given the following five propositions:
1. The graph of the function f(x) = 2a^(2x-1) - 1 passes through the point (1/2, -1);
2. The function f(x) is an odd function defined on R. When x >= 0, f(x) = x(x + 1). If f(a) = -2, then the real number a = -1 or 2;
3. If log_a (1/2) > 1, then the range of a is (1/2, 1);
4. If f(x) = f(4 - x) holds for any x in R, then the graph of f(x) is symmetrical about the line x = 2;
5. For the function f(x) = lnx, for any x1 ≠ x2 in its domain, f((x1 + x2) / 2) ≥ (f(x1) + f(x2)) / 2.

The sequence numbers of all correct propositions are _______.

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