
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 function $f(x)=(\frac{1}{3})^{x}-\log_{2}x$, where $0 < a < b < c$, and $f(a)f(b)f(c) < 0$. The real number $d$ is a zero of the function $f(x)$. Determine the possible sequence(s) of the following judgments: $①d < a$; $②d > b$; $③d < c$; $④d > c$. (Fill in the sequence number(s) of the correct proposition(s).)

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