
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
(1) Convert the base-5 number $1234_{(5)}$ to a decimal number, and then convert it to an octal number.  
(2) Use the Horner's method to calculate the value of the polynomial $f(x)=7x^{7}+6x^{6}+5x^{5}+4x^{4}+3x^{3}+2x^{2}+x$ when $x=3$.

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