
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
If ${x^6}={a_0}+{a_1}({2+x})+{a_2}{({2+x})^2}+⋯+{a_5}{({2+x})^5}+{a_6}{({2+x})^6}$, where $a_{0}$, $a_{1}$, $\cdots$, $a_{6}$ are real numbers.  
$(1)$ Find $a_{3}$;  
$(2)$ Find the value of $a_{1}+a_{3}+a_{5}$.

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