
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 $x^5(x+3)^3 = a_8(x+1)^8 + a_7(x+1)^7 + \ldots + a_1(x+1) + a_0$, find the value of $7a_7 + 5a_5 + 3a_3 + a_1$.

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