
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 polynomial ${\left(x+1\right)}^{3}(x+2{)}^{2}={x}^{5}+{a}_{1}{x}^{4}+{a}_{2}{x}^{3}+{a}_{3}{x}^{2}+{a}_{4}x+{a}_{5}$ , find the values of ${a}_{4}$ and ${a}_{5}$.

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