
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 ${(2x+1)^4}={a_0}+{a_1}x+{a_2}{x^2}+{a_3}{x^3}+{a_4}{x^4}$.  
$(1)$ Find the value of $\frac{{{a_1}}}{2}+\frac{{{a_2}}}{4}+\frac{{{a_3}}}{8}+\frac{{{a_4}}}{{16}}$;  
$(2)$ Find the value of $a_{1}+2a_{2}+3a_{3}+4a_{4}$.

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