
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

If organisms do not die but only divide, then the population will certainly never die out. 

The conditions are satisfied by the function whose graph is highlighted in the image.

$$
x(p)=\left\{\begin{array}{l}
1, \text { if } 0 \leq p \leq \frac{1}{2} \\
\frac{q}{p}, \text { if } \frac{1}{2}<p \leq 1
\end{array}\right.
$$

In our case $p=0.6>\frac{1}{2}$, therefore, $x=\frac{q}{p}=\frac{2}{3}$.

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