
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 $(1+2x)^{5}=a_{0}+a_{1}x+a_{2}{x}^{2}+a_{3}{x}^{3}+a_{4}{x}^{4}+a_{5}{x}^{5}$, then (${a}_{0}+{a}_{2}+{a}_{4}$) is equal to \_\_\_\_\_\_.

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