
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 $(x+1)^5 - x^5 = a + a_1 (x+4)^4 x + a_2 (x+1)^3 x^2 + a_3 (x+1)^2 x^3 + a_4 (x+1) x^4$, and $a_1$ (where $i=0,1,\ldots,4$) are constants, then find the value of $a_1 + a_3$.

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