
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
The filtration efficiency of the model of fresh air fan is $\frac{4}{5}$, and the concentration of particulate matter in the indoor air at $t=1$ is $\frac{3}{2}$ times that at $t=2$, given that the concentration of particulate matter in the indoor air as a function of time $t$ is described by $\rho \left(t\right)=\left(1-\lambda \right)\frac{m}{v_{0}}+\lambda \frac{m}{v_{0}}e^{-vt}$, find the approximate value of $v$.

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