
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
In the sequence $\{a_n\}$, $a_1=3$, $a_{n+1}-2a_n=0$. The general term $b_n$ of sequence $\{b_n\}$ satisfies the relation $a_nb_n=(-1)^n$ $(n\in \mathbb{N})$. Determine the value of $b_3$.

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