
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
City $C$, located between points $A$ and $B$, is supplied with gas from these points, which are 500 km apart. In each minute, $10000 \mathrm{m}^{3}$ of gas is extracted from reservoir $A$, and $12\%$ more is extracted from reservoir $B$. Additionally, there is a gas leakage of $4 \mathrm{m}^{3}$ per kilometer of pipeline. Knowing that city $C$ receives an equal amount of gas from reservoirs $A$ and $B$, find the distance between city $C$ and point $A$.

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