
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 a sequence $\{a_{n}\}$ that satisfies $\log _{2}a_{n+1}=1+\log _{2}a_{n}$, and $a_{1}=2$.  
$(1)$ Find the value of $a_{10}$;  
$(2)$ If the sequence $\{{a}_{n}+\frac{λ}{{a}_{n}}\}$ is strictly increasing, where $\lambda$ is a constant, find the range of values for $\lambda$.

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