
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
Consider the following four propositions:
1. The negation of the statement "For all $x$ in $\mathbb{R}$, $\cos(x) > 0$" is "There exists an $x$ in $\mathbb{R}$ such that $\cos(x) \leq 0$";
2. If $\log_{10}(a) + \log_{10}(b) = \log_{10}(a+b)$, then the maximum value of $a+b$ is 4;
3. A defined odd function $f(x)$ on $\mathbb{R}$ satisfies $f(x+2) = -f(x)$, then the value of $f(6)$ is 0;
4. Given a random variable $X$ that follows a normal distribution $N(1, \sigma^2)$, $P(X \leq 5) = 0.81$, then $P(X \leq -3) = 0.19$; identify the true propositions.

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