
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 the sequence $\{a_{n}\}$ satisfies $a_{1}=\frac{1}{2}$, $a_{n+1}=2a_{n}$. The product of the first $n$ terms of the sequence $\{\frac{1}{a_{n}}\}$ is $T_{n}$. Find $T_{5}$.

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