
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 a 5th-degree polynomial $f(x)=ax^5+2x^4+3.5x^3-2.6x^2-0.8$, when $x=5$, the value of $v_2=123.5$ is obtained using the Horner's method, calculate the value of $a$.

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