
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 $\{a_{n}\}$, $a_{1}=1$, for any positive integers $p$ and $q$, it satisfies $a_{p+q}=a_{p}+a_{q}$. For the sequence ${b}_{n}={2}^{{a}_{n}}$, if $b_{1}+b_{2}+\cdot \cdot \cdot +b_{k}=62$, determine the value of $k$.

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