
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 function $f(x)$ be defined on $\mathbb{R}^*$ and satisfy the condition $f(4)=1$. For any $x_1, x_2 \in \mathbb{R}^*$, it holds that $f(x_1x_2)=f(x_1)+f(x_2)$, and the function $f(x)$ is increasing on $\mathbb{R}^*$.
1. Find the value of $f(1)$.
2. If $f(3x+1) + f(2x-6) \leq 3$, determine the range of $x$.

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