
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
A company uses both newspaper and television advertising to promote sales of a certain product. According to statistical data, the relationship between the sales revenue $R$ (in ten thousand yuan) and the costs of newspaper advertising $x_1$ (in ten thousand yuan) and television advertising $x_2$ (in ten thousand yuan) is given by the 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 (i.e., the strategy that maximizes profit, where profit = sales revenue - advertising costs).
2. If there is no limit on the advertising costs, find the optimal advertising strategy.

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