
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
(The full score of this question is 12 points)

A company advertises a certain product through newspapers and television. According to statistical data, the relationship between the sales revenue $R$ (in ten thousand yuan) and the advertising expenses for newspapers $x_1$ (in ten thousand yuan) and for television $x_2$ (in ten thousand yuan) can be described by the following empirical formula: $R = -2x_1^2 - x_2^2 + 13x_1 + 11x_2 - 28$.

(1) If the total advertising budget is 5 ten thousand yuan, find the optimal advertising strategy. (That is, the strategy that maximizes profit, where profit = sales revenue - advertising expenses)

(2) If there is no limit on the advertising budget, find the optimal advertising strategy.

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