
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 that the function $f(x)$ is defined on the domain $\mathbb{R}^*$, and it satisfies the conditions $f(4)=1$, $f(x\_1⋅x\_2)=f(x\_1)+f(x\_2)$ for any $x\_1,x\_2∈\mathbb{R}^*$, and the function $f(x)$ is increasing on $\mathbb{R}^*$.
(1) Find the value of $f(1)$;
(2) If $f(3x+1)+f(2x-6)≤3$, find the range of $x$.

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