
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
We are given a real number  $a$ , not equal to  $0$  or  $1$ . Sacho and Deni play the following game. First is Sasho and then Deni and so on (they take turns). On each turn, a player changes one of the “*” symbols in the equation:
\[*x^4+*x^3+*x^2+*x^1+*=0\]
with a number of the type  $a^n$ , where  $n$  is a whole number. Sasho wins if at the end the equation has no real roots, Deni wins otherwise. Determine (in term of  $a$ ) who has a winning strategy

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