
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 propositions:
1. If $a$, $b$, $c$ are the solutions to the equations $x + \log_3x = 3$, $x + \log_4x = 3$, and $x + \log_3x = 1$, respectively, then $a > b > c$;
2. For an odd function $f(x)$ defined on $\mathbb{R}$ that satisfies $f(3 + x) + f(1 - x) = 2$, then $f(2010) = 2010$;
3. The equation $2\sin\theta = \cos\theta$ has 2 roots in $[0, 2\pi)$;
4. Given that $S_n$ is the sum of the first $n$ terms of an arithmetic sequence $\{a_n\}$ ($n \in \mathbb{N}^*$), if $S_7 > S_5$, then $S_9 > S_3$;

Among these, the numbers of the true propositions are

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