
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 heat engine "Lomonosov" 12341 receives heat in segment $1-2$ and gives it off in segment $3-4$. Therefore,

$$
\eta_{0}=1-\frac{Q_{34}}{Q_{12}}
$$

The engine "Avogadro" 1231 receives heat in segment $1-2$ and gives it off in segment $3-1$. Therefore,

$$
\eta_{1}=1-\frac{Q_{13}}{Q_{12}}
$$

The engine "Boltzmann" 1341 receives heat in segment $1-3$ and gives it off in segment $3-4$. Therefore,

$$
\eta_{2}=1-\frac{Q_{34}}{Q_{13}}
$$

By combining the three formulas above, we get

$$
\eta_{2}=\frac{\eta_{0}-\eta_{1}}{1-\eta_{1}}
$$

Given that $\eta_{1}<\eta_{0}$ and $\eta_{2}<\eta_{0}$ for all $\eta_{0}, \eta_{1}<1$, and that $\eta_{1}=(1-0.01 \alpha) \eta_{0}$, find the answer.

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