
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
Suppose $c$ is inversely proportional to $d$ and $c \cdot d = k$ for a constant $k$. Given $c_1$ and $c_2$ are two values of $c$ such that $\frac{c_1}{c_2} = \frac{4}{5}$, and corresponding values $d_1$ and $d_2$ for $d$, find the ratio $\frac{d_1}{d_2}$. Also, if $c_3 = 2c_1$, find the corresponding value of $d_3$.

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