
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 that ${(2x-1)^{5}}+{{(x+2)^{4}}={{a}\_{0}}+{{a}\_{1}}x+{{a}\_{2}}{{x}^{2}}+{{a}\_{3}}{{x}^{3}}+{{a}\_{4}}{{x}^{4}}+{{a}\_{5}}{{x}^{5}}}$, find the value of $|{a}\_{0}|+|{a}\_{2}|+|{a}\_{4}|$.

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