
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 $\left\{a_{n}\right\}$ is a geometric sequence with the first term 1 and a common ratio of 2, and $\left\{b_{n}\right\}$ is an arithmetic sequence with the first term 2 and a common difference of 5. The numbers that appear in both sequences are arranged in ascending order to form the sequence $\left\{x_{n}\right\}$. Find $x_{100}$.

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