
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
Given that nonzero reals  $a,b,c,d$  satisfy  $a^b=c^d$  and  $\frac{a}{2c}=\frac{b}{d}=2$ , compute  $\frac{1}{c}$ .


*2021 CCA Math Bonanza Lightning Round #2.2*

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